Hours after he spoke, a 9-year-old girl and her 34-year-old mother were woken in the predawn hours by the wail of an air-raid alarm in Kyiv, the police said. The two raced to what they thought would be the safety of a bomb shelter at a children’s hospital in the city, but, according to Mayor Vitali Klitschko, they died just outside the door.

Russian ballistic missiles had been flying toward the city at around five times the speed of sound as the two stood outside the hospital building, the police said. Just minutes after the alarm sounded, according to the mayor, one of the missiles was struck by a Ukrainian interceptor missile in the skies above, and the child and her mother were killed by the fiery debris. As dawn broke, the child’s grandmother arrived to identify the bodies.

The girl’s death, in the early hours of International Children’s Day in Ukraine, served as a reminder that the most innocent are among those paying a high price in the war. It also sparked renewed outrage across Ukraine. Mr. Klitschko said that events planned in the city to celebrate Children’s Day had been canceled, and that an investigation was underway into why the door had been closed.

A 33-year-old woman was also killed by falling debris nearby, according to the police, and at least 16 people were injured, the mayor said. Windows in the surrounding homes and apartments were shattered and blown out. In other parts of the city, crews were still racing to assess the damage on Thursday morning.

United Nations human rights monitors say that at least 525 children have been killed across Ukraine in the war, and at least 1,047 injured.

In his remarks the day before, Mr. Zelensky had made an emotional appeal, saying the killing of children should not become normalized.

“Russia killed — and this is why I will use such wording — Russia killed 483 children at least,” he said. “It killed them. This is not something that can be called ‘they were victims of Russian aggression’ or ‘they died as a result of the armed conflict.’ No, Russia killed these children. Russia maimed almost 1,000 more children.”

He read from the diary of another child caught in the maelstrom of war: Yehor, a 9-year-old boy from the city of Mariupol in southern Ukraine.

“I have a wound on my back, the skin is torn off,” the child wrote while the city was under siege by Russian forces last year, Mr. Zelensky relayed. “My sister has a head wound. My mom has flesh torn out of her arm and a wound on her leg.”

“My grandmother, Galya, two dogs, and my favorite city of Mariupol died,” the boy wrote, according to Mr. Zelensky.

The Ukrainian leader said that his country was fighting for the rights of all children so that “there will never again be new diaries by Anne Frank and Yehor from Mariupol.”

“Where it is safe,” he said. “Where it is free.”