Parents holding babies walked in the street outside the hospital on Monday, dazed and sobbing after the rare daylight aerial attack. Windows had been smashed and panels ripped off, and hundreds of Kyiv residents were helping to clear debris.
President Volodymyr Zelenskiy, who stopped in Poland before heading off to Washington for a NATO summit, put the death toll at 37, including three children. More than 170 were injured.
But tallies of casualties from the sites of attacks in different regions totalled at least 41.
A 10-year-old girl at the site of Okhmatdyt children's hospital hit by Russian missiles, in Kyiv. (AP PHOTO)
Writing on the Telegram messaging app, Zelenskiy said more than 100 buildings had been damaged, including the children's hospital and a maternity centre in Kyiv, children's nurseries and a business centre and homes.
"The Russian terrorists must answer for this," he wrote.
"Being concerned does not stop terror. Condolences are not a weapon."
The Interior Ministry said there had also been damage in the central cities of Kryvyi Rih and Dnipro and two eastern cities.
The government proclaimed a day of mourning on Tuesday for one of the worst air attacks of the war, which it said demonstrated that Ukraine urgently needed an upgrade of its air defences from its Western allies.
Air defences shot down 30 of 38 missiles, the air force said.
An online video obtained by Reuters showed a missile falling towards the children's hospital followed by a large explosion. The location of the video was verified from visible landmarks.
The Security Service of Ukraine identified the missile as an Kh-101 cruise missile.
Kyiv's military authorities said 27 people had died in the capital, including three children, and 82 were wounded in the main missile volley and a strike that came two hours later.
Kyiv Mayor Vitali Klitschko said the attack was one of the largest of the war, causing damage in seven city districts. The Health Minister said five units of the children's hospital were damaged and children were evacuated to other facilities.
Eleven were confirmed dead in the Dnipropetrovsk region and 68 were wounded, regional officials said. Three people were killed in the eastern town of Pokrovsk where missiles hit an industrial facility, the governor said.
Zelenskiy, addressing a news conference in Warsaw alongside Polish Prime Minister Donald Tusk, called on Kyiv's Western allies to give a firm response to the attack.
"We will retaliate against these people, we will deliver a powerful response from our side to Russia, for sure. The question to our partners is: can they respond?" Zelenskiy said.
The attack came a day before leaders of NATO countries were due to begin a three-day summit, with the war in Ukraine one of the focuses.
US President Joe Biden said that Moscow's deadly missile strikes in Ukraine, including on the children's hospital in Kyiv, were "a horrific reminder of Russia's brutality".
A Ukrainian soldier carries a part of the missile after a Russian attack destroyed children hospital (AP PHOTO)
In a statement released by the White House, Biden added that Washington and its NATO allies would be announcing new measures to strengthen Ukraine's air defences.
Diplomats said the United Nations Security Council would meet on Tuesday at the request of Britain, France, Ecuador, Slovenia and the United States.
Moscow has repeatedly denied targeting civilians and civilian infrastructure, although its attacks have killed thousands of civilians since it launched its invasion in February 2022.
