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When the shelling starts, the people who remain in the devastation of Avdiivka hardly flinch. In truth, the shelling barely stops. In this ravaged town in eastern Ukraine, the thud of Russian artillery reverberates every minute or two.

“Do you hear? It’s flying,” one resident said as a rocket passed overhead. “Then there is a boom,” he added as it detonated.

As Russia wages an offensive across a broad front in eastern Ukraine, in the last few weeks it has intensified its bombardment of Avdiivka and outlying villages, near the Russian-held regional capital, Donetsk. The barrage has left Avdiivka, already battered and largely abandoned by residents after a year of war, without power, running water or intact shelter for its civilian holdouts.

Moscow’s monthslong advance has been slow: It has yet to capture any major towns. But it is also devastating, claiming casualties by the tens of thousands and reducing the places in its path to ruins.

On Monday, the Ukrainian government barred civilians from entering the town, citing safety concerns; the top official in Avdiivka, Vitaliy Barabash, called it “like a site from postapocalyptic movies.” A team of New York Times journalists visited on Monday just before the ban was announced.

Residential communities were strewn with the ruins of blasted buildings, pavement and vehicles, making streets nearly impassable by car. Schools, health clinics, shopping centers and apartment blocks had been left with gaping holes. Chunks of unexploded ordnance protruded from the streets.

The remaining residents were living in damp, candlelit basements beneath Soviet-era apartment buildings, pervaded by stifling smells, where they had set up beds, makeshift kitchens, bookshelves and small Orthodox shrines. Ukrainian police went from basement to basement, trying to persuade civilians to evacuate.

The longtime focus of the Russian offensive, Bakhmut, lies 34 miles to the northeast, and Moscow has not let up in its assault there, even as fighting escalates elsewhere along the front, officials on both sides said on Tuesday. Russian forces have fought for nine months to seize Bakhmut, advancing from three directions and recently taking control of the eastern side of the city, but Ukrainians have held fast on the western side.

“They are not giving up their attempts to surround and capture the city,” Gen. Oleksandr Syrsky, commander of Ukrainian ground forces, said on the Telegram messaging app.

Denis Pushilin, the Russian-installed leader of the Donetsk region, said on Russian state television that the Kremlin’s forces were pushing ahead, wresting control from the Ukrainians of a metals factory on the western side of Bakhmut, a claim that could not be independently verified.

The battle there has killed or wounded thousands, and officials on both sides have claimed that the carnage has served to wear down its enemy.

Britain’s Defense Ministry said in an intelligence update on Tuesday that a parallel effort to encircle and capture Avdiivka had become a high Russian priority but had “made only marginal progress at the cost of heavy losses in armored vehicles.”

The Ukrainian military’s General Staff said on Tuesday that Ukrainian forces had repelled 62 attacks in the previous 24 hours in Bakhmut, Avdiivka and Marinka, another eastern town nearby.

With more powerful Western weapons arriving and fresh troops being conscripted, Ukraine is widely expected to launch a counteroffensive soon, hoping to retake Russian-held territory. Analysts say the main push is likely to be farther west, in the Kherson and Zaporizhzhia regions.

In Zaporizhzhia, “there is a quite obvious increase in the number of troops on both sides, military equipment, etc.,” Rafael Mariano Grossi, the chief nuclear-energy watchdog for the United Nations, said in an interview on Tuesday. “Our teams are also observing and hearing and seeing more military activity, including detonations.”

Mr. Grossi is in the region and plans on Wednesday to visit the Zaporizhzhia Nuclear Power Plant, seized by Russia last year. It has been damaged repeatedly in the fighting, raising fears of an incident that could cause a major radiation release. Mr. Grossi is trying to negotiate an agreement to make the plant and its surroundings a demilitarized zone.

Ukrainian officials say the danger there is elevated by the Russian occupiers abusing the plant’s short-handed Ukrainian staff and stationing troops and weapons at the plant, which the Russians have denied.

Russia has repeatedly hinted at another kind of nuclear danger: the use of nuclear weapons. On Sunday, Mr. Putin said Russia could soon station such weapons in Belarus, its ally, which borders Ukraine to the north. The government of Belarus said on Tuesday that it would be open to Russian tactical nuclear weapons on its soil.

Western analysts say such talk is most likely bluster and note that Russia already has the capacity for nuclear strikes in Ukraine, but the threats keep the topic on Ukrainian and Western minds.

The United States has informed Russia that it will no longer share data on American nuclear forces as required under the New START nuclear arms-control treaty, Biden administration officials said on Tuesday. Mr. Putin said last month that Russia was suspending its participation in the treaty, and it had already blocked American inspections of its arsenal under the treaty.

Despite the suffering and risks, neither Moscow nor Kyiv has shown serious interest in ending the war, except on terms the other side calls unacceptable. President Vladimir V. Putin of Russia has said that his top priority is conquest of the eastern Donetsk and Luhansk regions, which his forces mostly control. His government claims to have annexed to Russia those two provinces, and also Zaporizhzhia and Kherson, though it does not hold the entirety of any of the four.

President Volodymyr Zelensky of Ukraine has said his country will accept nothing less than the Russians either withdrawing or being expelled from all Ukrainian territory. Stopping the fighting before that, Ukrainian and American officials say, would only cement into place Russia’s illegal gains.

Secretary of State Antony J. Blinken reiterated that position on Tuesday in a thinly veiled swipe at a proposal by China, Russia’s most important ally, that includes a cease-fire. Though he did not mention China by name, Mr. Blinken warned against any plans that would simply give Russia room “to rest and refit and then reattack,” he told foreign ministers in a video meeting of foreign ministers from around the world.

“What seems to be appealing on the surface — who wouldn’t want the guns to be silent? — can also be a very cynical trap that we have to be very, very careful of,” he added.

Where the guns are loudest, near the front lines across eastern and southern Ukraine, most residents fled long ago, but some remain. That is evident in Avdiivka, which lies just outside Donetsk city, controlled by Russians since the Kremlin’s separatist proxy forces seized it in 2014.

Out of 30,000 people who lived in Avdiivka before the full-scale Russian invasion, Ukrainians say only hundreds remain. They mostly stay underground, where it is safer. One retiree said she hadn’t been outside for five months.

People have stayed behind for various reasons. Some say they are too ill, others too attached to their prewar lives. Most are middle-aged and older.

“I’ve been living here for 43 years. How can I leave Avdiivka?” said one older resident, Polina, who emerged from a basement to drop off cat food for a neighbor and check on damage to her apartment. Like others interviewed for this article, she gave only her first name, fearing for her safety.

“At my old age, I don’t want to hop around to different apartments somewhere else,” she added.

Nearby, a building was still smoking after a recent rocket strike.

Still others say they are too poor to move. Some appear psychologically paralyzed after months of shelling. Many simply sit on their beds and stare blankly.

And in a region with strong ties to Russia, loyalties are sometimes divided. Two older residents appeared to support Russia and blamed both sides of the war for shelling their community.

Many residents knew a pair of police officers who visited on Monday, from previous visits, and were used to their attempts to persuade them to leave.

One mother, Natalya, agreed to be evacuated with her 3-year-old daughter, Marina. She was distraught as she packed their few belongings into plastic bags and said she had no money to start a new life.

But most of those approached rebuffed the officers, then scuttled back down to their basements and slammed the doors.

Reporting was contributed by Matthew Mpoke Bigg from Kyiv, Edward Wong from Washington and Enjoli Liston from London.

WASHINGTON — A top regulator at the Federal Reserve on Tuesday blamed Silicon Valley Bank’s executives for its collapse and provided little explanation for why supervisors had failed to stop its demise, saying that the central bank was examining what went wrong.

Michael S. Barr, the Fed’s vice chair for supervision, testified for more than two hours before the Senate Banking Committee alongside Martin Gruenberg, chairman of the Federal Deposit Insurance Corporation, and Nellie Liang, the Treasury’s under secretary for domestic finance.

They faced skeptical questioning from lawmakers about why their agencies — in particular the Fed, which was Silicon Valley Bank’s main regulator — had not done more to stop the bank from imploding. Democrats pressed the officials on whether gaps in regulation had allowed problems in the banking system to build after rollbacks under the Trump administration. Republicans, by contrast, blasted Fed supervisors for either missing obvious risks or not addressing them effectively.

It is unclear whether the intense scrutiny will spur any new laws or changes to existing ones, especially in a divided Congress. But the episode is likely to prompt regulatory and supervisory changes at the Fed. The central bank is conducting an investigation into how it failed to stop growing vulnerabilities at the bank. Mr. Barr suggested repeatedly on Tuesday that tighter regulation and supervision would most likely be the result of that inquiry, which is set to conclude by May 1.

Fed supervisors were aware of at least some of the problems plaguing Silicon Valley Bank beginning in late 2021, though it was unclear how detailed of a grasp they had on the risks. Mr. Barr said on Tuesday that he learned of some of the worst vulnerabilities at the bank only in February, just ahead of its collapse.

Lawmakers from both parties questioned why the Fed wasn’t more successful at forcing the bank’s leadership team to change its practices, which included a misguided and unprotected bet that interest rates would remain low. Even as the Fed was still vetting what happened, Mr. Barr said, poor management at Silicon Valley Bank allowed its weaknesses to build to a point that the bank failed on March 10.

“Fundamentally, the bank failed because its management failed to appropriately address clear interest rate risk and clear liquidity risk,” Mr. Barr said. “The Federal Reserve Bank brought forward these problems to the bank, and they failed to address them in a timely way — that exposure led the firm to be highly vulnerable to a shock.”

Silicon Valley Bank invested heavily in long-term bonds that became less valuable as interest rates rose last year. And it did not hold protection against higher borrowing costs. When it sold some of its assets and disclosed losses in early March, the announcement spooked depositors — many of whom had accounts in excess of the $250,000 that is guaranteed by the F.D.I.C.

Customers, afraid of losing their money, raced to pull out their deposits: $42 billion left the bank on Thursday, March 9, and Mr. Barr said another $100 billion was about to head out the door the next day, when the bank collapsed and was seized by the F.D.I.C.

The bank’s failure set off a chain reaction that has coursed through the global banking system in the weeks since. Regulators tried to find a buyer for SVB that weekend but could not: Of two bids from interested banks, Mr. Gruenberg said, one was ineligible because the bank’s board had not approved the offer, and the other was not a good enough deal for the government to legally accept it.

To contain the fallout, that Sunday evening officials made a sweeping rescue — announcing that another firm, Signature Bank, had failed but promising that the government would make sure depositors were paid back in full. The Fed simultaneously set up an emergency lending program that gives banks access to cash in a pinch in exchange for bonds and other securities.

The efforts to stop depositors from pulling their cash did not immediately stem the bleeding. First Republic took an injection of capital from other banks, and in Europe, the Swiss lender Credit Suisse was rushed through a takeover by UBS.

But in recent days, government officials have said deposit outflows are stabilizing in the United States. Regulators reiterated on Tuesday that the banking system was sound — and said the actions they had taken were necessary to ensure that it remained so.

“I think there would have been a contagion,” Mr. Gruenberg of the F.D.I.C. said.

The turmoil brought to light a number of problems in the American financial system, including the question of whether federal deposit insurance is correctly calibrated.

A big share of U.S. deposits are not protected by the government, and the businesses or individuals holding those accounts are more likely to pull their money at the first sign of trouble. The F.D.I.C. explicitly insures up to $250,000, but the government’s rescue calls into question whether it is implicitly backing all deposits.

In the case of the two failed banks, officials invoked a rule that allowed regulators to pay out even uninsured depositors — something they would not usually be able to do — if the fallout otherwise posed a risk to the entire system. Ms. Liang reiterated on Tuesday that the government would be prepared to take such steps again, if they were deemed necessary.

“We have used important tools to act quickly to prevent contagion,” Ms. Liang said. “And they are tools we would use again if warranted to ensure that Americans’ deposits are safe.”

Mr. Gruenberg said regulators would also be looking at a longer-term fix to the way deposits were insured, including coverage levels.

“The decision to cover uninsured depositors at these two institutions was a highly consequential one that has implications for the system,” Mr. Gruenberg said. “We want to try to be responsive on that.”

Still, much of the hearing focused not on deposit insurance, but on bank oversight.

Senators wanted to know whether Silicon Valley Bank failed because supervisors and regulators at the Federal Reserve Bank of San Francisco and the Fed’s board in Washington dropped the ball, or whether they lacked the authority to react aggressively enough.

Democrats suggested on Tuesday that the problems tied back to deregulation under the Trump administration and greed on the part of Silicon Valley Bank’s executives.

“Monday morning quarterbacking aimed only at the actions of regulators this month is as convenient as it is misplaced,” Senator Sherrod Brown, Democrat of Ohio, said at the start of the hearing.

Republicans also fired shots at bank managers, but said Fed supervisors were to blame for allowing problems to slip through the cracks.

“What were the supervisors thinking?” Senator Tim Scott, Republican of South Carolina, said during the hearing. He implied, with no evidence, that the San Francisco Fed might have overlooked risks at Silicon Valley Bank because they shared a focus on climate change.

Republicans and bank lobbying groups have tried to minimize the role that regulatory changes made during the Trump administration — which relaxed rules for midsize banks — played in Silicon Valley Bank’s demise. But Mr. Barr made it clear on Tuesday that the episode was likely to result in tougher oversight.

Randal K. Quarles, Mr. Barr’s predecessor, carried out a number of changes to bank oversight before stepping down in October 2021. Without the tweaks, Silicon Valley Bank would almost certainly have come under more intense scrutiny from Fed supervisors earlier.

Mr. Barr, who was nominated by President Biden and took his post in July, said those changes would get a second look.

“The decision to set those lines by asset size and other risk factors was made back in 2019,” Mr. Barr said. “I believe we have substantial discretion to alter that framework.”

He said the Fed would revisit how firms were bucketed by size when it came to supervision and regulation. And he acknowledged that the Fed would look into whether its bank examiners had taken reasonable actions to address problems at the bank.

He added that “the staff are reviewing the steps that supervisors took, and whether they should have taken more aggressive action.”

The F.D.I.C. is reviewing the collapse of Signature Bank, which it oversaw, and the Fed’s inspector general on March 14 opened a review of the conduct of the Fed Board of Governors and the Federal Reserve Bank of San Francisco’s supervision.

Some lawmakers want more. A group of Democrats on Tuesday asked the Government Accountability Office to examine the supervisory practices of bank regulators.

“The collapse of these banks brings into focus matters related to the supervision and examination of our nation’s large banks,” the letter said.

Emily Flitter, Alan Rappeport and Jim Tankersley contributed reporting.