A gigantic, roiling cloud of black smoke swirled up from a parking lot of burning cars, as residents milled about on a sidewalk in distress, and police and fire vehicles careened past. Then the scene became more chaotic.

“Shelter! shelter!” a policeman yelled. A thin, buzzing noise, like a chain saw running in the distance, wafted down from the sky. Another Russian exploding drone, like the one that had just hit the parking lot, was flying overhead. People ran for cover.

“It’s like this every day,” said the mayor, Artem Kobzar, who had been visiting the site in Sumy, Ukraine, and dashed into the open doorway of an apartment building. “Everybody in Ukraine wants peace,” he said. “But you see, in Sumy, we don’t have a day or night of calm.”

That bombardment came on Monday, a day after two ballistic missiles struck a central neighborhood of the city on Palm Sunday shortly after 10 a.m., killing 34 civilians, including two children, and wounding another 117, according to the Sumy City Council. Russia said it had struck a military target; a Ukrainian regional governor said a military awards ceremony had taken place in the city that day.

The Palm Sunday bombardment came more than two months after President Trump started cease-fire talks with a phone call to President Vladimir V. Putin of Russia. And in recent days it has become an argument in Ukraine and elsewhere that those talks are failing. In Sumy, the attack has set off preparation for a possible new Russian ground assault in this region.

Last month, Mr. Trump briefly halted military and intelligence aid to pressure Ukraine into the cease-fire talks while seeking to bring Russia to an agreement with incentives of renewed economic cooperation. Ukraine has agreed to an unconditional cease-fire while Russia is bargaining for sanctions relief and other concessions.

In remarks in the Oval Office on Monday, Mr. Trump blamed the war on former President Joseph R. Biden Jr., President Volodymyr Zelensky of Ukraine and Mr. Putin. The war would not have begun, he said, “if Biden were competent, and if Zelensky were competent, and I don’t know that he is.”

“We had a rough session with this guy,” he added. “He just kept asking for more and more.”

Of the cease-fire talks, he said, “I want to stop the killing, and I think we’re doing well in that regard.”

European leaders including President Emmanuel Macron of France flatly condemned the civilian deaths in the Sumy strike. Mr. Trump, speaking to reporters on Air Force One on Sunday, called the attack a “horrible thing.” He also said, “I was told they made a mistake.” Mr. Zelensky has pointed to the loss of life as proof that Russia is not serious about peace negotiations.

“Thirty-four days ago, Ukraine responded positively to the U.S. proposal for a full and unconditional cease-fire,” Mr. Zelensky said on Monday. Russia, he said, “remains focused on continuing the war.”

Ukraine is reporting a rise in drone strikes across the country, and Sumy is particularly on edge — and disillusioned in settlement negotiations. The feeling of living under barrage in this city — a picturesque jumble of hundreds-of-years-old churches and apartment blocks along leafy avenues — is of fear, ceaseless tension and frayed nerves. Every week, one building or another is blown to smithereens from a bolt out of the sky.

The city, in northeastern Ukraine, is both near the border and a hub of Ukrainian military activity, and lies under routes flown by exploding drones heading deeper into Ukraine. The rattle of their engines in the sky is daily and nightly backdrop to life here. Few believe in a cease-fire.

Out on the streets on Monday, at the site of the Palm Sunday attack, a backhoe scraped layers of debris from a collapsed building, as rescuers looked for additional victims, stirring clouds of dust. Threats of air attacks repeatedly disrupted the cleanup work in the area, a sprawl of burned cars and splays of brick on the sidewalks. Mourners walked over tinkling shards of broken glass and bloodstains on the pavement to lay flowers on a memorial.

Few here saw the mistake that Mr. Trump referred to, given that two ballistic missiles were fired.

The missiles streaked in about three minutes apart, in apparent coordination for a so-called double-tap strike. The tactic of firing two munitions in succession at the same target can be intended to hit emergency medical workers or people staggering out of rubble, maximizing casualties.

Double taps are horrifying experiences for those caught in them.

On Sunday, amid the dust and shrieking car alarms after the first strike, Viktoria Rudyka, 37, knelt on the sidewalk pressing her hands on a hole in the chest of her 6-year-old daughter, Elina, she said in an interview on Tuesday. Like others tending to those wounded, she could not run from the scene. A passing car screeched to a stop, she said, and loaded mother and daughter to take them to the hospital — just on time, as the second tap hit and rained debris over the scene, with rubble bouncing off the car roof. Doctors removed a metallic shard from the girl’s lung.

Russia’s foreign minister, Sergey V. Lavrov, said Sunday’s strike hit a meeting of Ukrainian and Western military officials. The governor of the Sumy region, Volodymyr Artyukh, said he had participated in a ceremony awarding honors to soldiers on Sunday. That suggested a possible target for the strike, despite the crowds of civilians nearby. On Tuesday, Mr. Zelensky’s political party said the government had dismissed Mr. Artyukh, but did not clarify why.

Ukraine’s general staff headquarters said on Tuesday that it had retaliated for the Palm Sunday attack with a strike on the Russian headquarters of the unit it said had launched the missiles. The strike could not be independently confirmed.

Tetyana Marunchak, a kindergarten teacher, was returning from communion at church on Sunday when her son, Ivan, who is 13, asked to meet a friend to play. After the first explosion, she said in an interview on Tuesday, she called him. He said he was unhurt. But after the second explosion, he did not pick up.

Ivan was caught in a spray of jagged, metallic shards of shrapnel that burst from the missile, piercing his lung and ripping through his leg. His friend, who had been hit in the stomach with shrapnel, nonetheless ran for help.

“The kids are not guilty,” Ms. Marunchak said, crying at his hospital bedside on Tuesday. She said her son’s leg might be amputated. “I don’t believe in a cease-fire anymore,” she said. Of Mr. Trump’s and Mr. Putin’s engagement in talks she said, “They are just devils.”

Monday’s bombardment in the parking lot did not involve a double tap, but Russia has in recent months attacked Sumy with a variety of such strikes. Typically, a second missile or drone is fired with a gap of about 20 minutes, to catch emergency medical workers as they arrive and fan out, said Oleh Strilka, a spokesman for the State Emergency Service of Ukraine. But variations abound, and the risks are great.

A double-tap strike last month, for example, targeted the entrance to a bomb shelter at a hospital in a nearby town to hit people running for safety, Mr. Strilka said, in an account verified with a neighbor. The second strike blew in the bomb shelter doors, trapping people inside, though nobody was killed. Closer to the border, Russia has targeted fire trucks with small exploding drones that hover in wait over roads after artillery shelling sparks fires, Mr. Strilka said. Fire crews have mostly stopped responding.

On Monday, four employees of a Sumy coffee shop called Be Happy walked together to lay pink and white roses on a pile of bouquets amid the debris of the Palm Sunday strike site, where a cook and a pastry chef had been killed. The group cried and hugged one another.

There are no signs of a cease-fire in Sumy, said Diana Khaitova, 22, a server, who on the day of the strike found the bodies of her dead colleagues lying on a street. People in the city, she said, “are just always afraid.”