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Russia struck cities across Ukraine on Monday with a missile barrage that killed 31 people and heavily damaged a Kyiv children's hospital in an assault condemned as a ruthless attack on civilians.

Dozens of volunteers, doctors and rescue workers were digging through debris of a part of Okhmatdyt paediatric hospital in a desperate search for survivors after the rare day-time bombardment, AFP journalists on the scene saw.

The first responders ran for cover when sirens and a explosion sounded after the initial strikes - a repeat attack that left four dead at a maternity hospital in a separate district of Kyiv, emergency services said.

President Volodymyr Zelensky said Russian forces fired more than 40 missiles toward at least five major civilian hub, mainly in the south and east of the country, as well as the capital.

Zelensky arrived in Poland as news of the strikes broke to sign a security deal with Prime Minister Donald Tusk in Warsaw, where the leaders held of minute of silence for the victims.

The Ukrainian leader in Warsaw called on allies to deliver "a stronger response to the blow that Russia has once again delivered on our population, on our land and on our children."

France denounces 'barbaric' attack

The UN condemned the wave of strikes saying it was "unconscionable that children are killed and injured in this war," while the EU's Josep Borrell slammed Russia for "ruthlessly" targeting civilians.

France condemned the attacks, with the foreign ministry calling the bombardment of a children's hospital in Kyiv "barbaric".

Kyiv said the children's hospital had been struck by a Russian cruise missile and claimed that it contained components produced in NATO member countries.

Russia however claimed the extensive missile damage in Kyiv was in fact caused by a Ukrainian air defence missile.

Moscow said its forces had struck their "intended targets", which it added were only defence industry and military installations.

Natalia Svidler, 40, was in the hospital at the time of the strike with her two-year-old son, who was due to have surgery this week, when the air raid sirens sounded.

"The nurses told us to go down to the basement. After a while we heard a loud rumble and then the ceiling in the basement collapsed a little," she said at the scene.

"Everyone got very scared, of course. Everyone started screaming and running," she told AFP.

Officials in Kyiv said the attack had also damaged several residential buildings and an office block in Kyiv where AFP reporters saw cars on fire and shredded trees in charred courtyards.

Energy sites 'destroyed, damaged'

DTEK, Ukraine's largest private energy company, said three electrical substations had been destroyed or damaged in Kyiv in the attack - the latest in series of strikes that have halved the country's energy generation capacity in recent months, compared to one year ago.

Zelensky said that there were an unknown number of people trapped under the rubble of the children's hospital. An AFP reporter saw one body at the scene, covered with a blanket.

Emergency officials said 20 people had been killed in the barrage that hit Kyiv and another 38 were wounded.

Russian forces have repeatedly targeted the capital with massive barrages since Moscow invaded Ukraine in February 2022, and the last major attack on Kyiv with drones and missiles was last month.

Must respond 'with force'

In Zelensky's hometown Kryvyi Rig, which has been repeatedly targeted by Russian bombardment, the strikes killed at least 10 and wounded over 41, officials there said.

In Dnipro, a city of around one million people in the same region, one person was killed and six more were wounded, the region's governor said, when a high rise residential building and petrol station were hit.

And in the eastern Donetsk region, where Russian forces have taken a string of villages in recent weeks, the regional governor said three people were killed in Pokrovsk - a town that had a pre-war population of around 60,000 people.

"This shelling targeted civilians, hit infrastructure, and the whole world should see today the consequences of terror, which can only be responded to by force," the head of Ukraine's presidential administration, Andriy Yermak, wrote on social media.

Zelensky and other officials in Kyiv have been urging Ukraine's allies to send more air defence systems, including Patriots, to the war-battered country to help fend off deadly Russian aerial bombardment.

"Russia cannot claim ignorance of where its missiles are flying and must be held fully accountable for all its crimes," Zelensky said in another post on social media.