Even in a city where people have adapted the routines of ordinary life to wartime, the barrage of Russian missiles that rained on the Ukrainian capital, Kyiv, in the predawn hours Tuesday, was a reminder that while the fighting has been concentrated hundreds of miles east, the city still has a Russian bull’s-eye on it.

It was the second day that ballistic missiles began roaring in, beginning shortly after 11 a.m. Monday — a rare daytime barrage that sent city residents racing for cover — and were quickly shot down. Then, the attacks erupted again early Tuesday, making it clear that even as Kyiv, aided by Western allies, builds up its air-defense system, Russian forces are intent on testing for soft spots.

They have changed the timing of bombardments, the combination of weapons used and the trajectories of missiles and drones, lately flying them low along riverbeds and through valleys to avoid detection, Ukrainian officials say.

Russia is trying to “confuse and mislead our air defense system,” Yurii Ihnat, a spokesman for Ukraine’s Air Force Command, said in an appearance on national television over the weekend. “It uses the topography of the area to disappear from radars.”

On Monday, 11 ballistic missiles targeted Ukraine, and 11 were intercepted, Ukrainian officials said. But debris from the in-air collisions caused fires and other damage, as terrified Ukrainians looked to the clear-blue skies of their densely populated city to witness a battle unfolding with explosive force.

Schoolchildren shouldering backpacks ran in terror after the booms resounded on one city street, a video widely shared by Ukrainian officials on social media showed.

“How they cried, how they screamed!” said Natalia Nevidoma, 53, who was cleaning a restaurant’s front porch as teachers led small children past the entrance. “You know, it’s so painful and scary.”

The mayor of Kyiv, Vitali Klitschko, warned residents in a post on the Telegram messaging app not to leave shelters. About 20 residents of a high-rise building in Kyiv were also being evacuated early Tuesday after falling debris from a destroyed Russia-launched air target ignited a fire, Mr. Klitschko added. One person died, and a woman was injured from the falling debris, according to the mayor. Another injury was also reported from the missile bombardment, but details were not immediately available.

The barrage drew an immediate condemnation from the Ukrainian government. Russian forces “struck a peaceful city during the day, when most of the residents were at work and on the streets,” Serhii Popko, the head of the Kyiv regional military administration, said in a statement.

“In other words,” Mr. Popko said, “the Russians are clearly demonstrating that they are aiming to destroy the civilian population.”

Russian officials have often denied targeting civilian areas. They said the strikes on Monday had been aimed at air bases, and Ukrainian officials said Moscow did hit at least one military installation, damaging an airfield in Khmelnytskyi, western Ukraine. “Five aerial vehicles went out of service,” the Khmelnytskyi Regional Military Administration said in a statement.

The stepped-up assaults on Kyiv of the past weeks rival those during some of the most dire moments of the war for the city of 3.6 million. In Kyiv, as well as elsewhere in Ukraine, Moscow has been steadily deploying attack drones, ballistic missiles and cruise missiles, Ukrainian officials say. On Sunday, Ukrainian air defense teams repelled Russia’s largest drone attack on Kyiv since the start of the war.

Kyiv was not the only target on Monday.

The Ukrainian Air Force said that Russia had fired up to 40 cruise missiles and 35 Iranian-made attack drones before dawn on Monday. It said 37 of the missiles and 29 of the drones had been shot down. But one missile hit a village in the Kharkiv region, Kivsharivka, wounding at least three people, according to the local military administration.

In Kyiv, emergency crews were dispatched to extinguish fires caused by falling debris. The Kyiv regional military administration said it was working to clear at least six locations around the capital, including a major roadway.

Kseniia Khyzhniak, 35, had been using her day off work to catch up on a TV series when the sirens sent her racing to her children’s school.

“I’m looking at the sky, and the air defense rocket is flying there,” Ms. Khyzhniak said. There was one bang, and then another as her two young children ran to meet her and they raced to the shelter, holding hands, she said.

“Hurry up!” Ukrainians standing at the entrance yelled, waving them in, she said.

Oleksandr, 40, a technology worker who declined to provide his last name, said he, too, had found himself heading for shelter — even if he was not really sure what the point was.

“Getting hit by the car and dying is more probable in Kyiv at the moment than dying of shelling, mathematically,” he said. “But I can’t order my body how to react, you know?”

Anatolii Semenov, a 68-year-old retiree at home, was more philosophical.

“I didn’t go to the shelter,” he said. “I never do. There is a Ukrainian saying: ‘What has got to be has got to be.’ My father taught me that.”