Russia has attacked cities across Ukraine with a missile barrage that killed more than three dozen people and ripped open a children's hospital in Kyiv.

Dozens of volunteers including hospital staff and rescue workers dug through debris from the Okhmatdyt paediatric hospital in search for survivors after the rare day-time bombardment on Monday.

President Volodymyr Zelensky said Russia launched dozens of missiles toward five towns and cities in southern and eastern Ukraine as well as the capital.

At least 37 people were killed, including three children, with more than 170 wounded, Zelensky said.

The strikes damaged nearly 100 buildings, including multiple schools and a maternity hospital, he added. The air force said air defence systems downed 30 projectiles.

"It is necessary to shoot down Russian missiles. It is necessary to destroy the Russian combat aircraft on its bases. It is necessary to take strong steps that will not leave any security deficit," Zelensky said ahead of a Nato summit where arming Ukraine's air defences is expected to top the agenda.

Zelensky called for an emergency meeting of the United Nations Security Council over the barrage and urged Ukraine's allies to deliver "a stronger response" to Russia's attack.

Following the strikes, US President Joe Biden on Monday promised "new measures" to boost Ukraine's air defences.

"Together with our allies, we will be announcing new measures to strengthen Ukraine's air defences to help protect their cities and civilians from Russian strikes," Biden said.

Meanwhile, a Ukrainian drone attack spurred a fire at a power substation and at an oil depot in Russia's Volgograd region, the governor of the region in southern Russia said on Tuesday.

"Air defence and electronic warfare forces suppressed a UAV [unnamed aerial vehicle] attack on the territory of the Volgograd region," Andrei Bocharov, the governor, said in a post published on the Telegram channel of the region's administration.

"As a result of falling UAV debris, fires broke out at a substation in Frolovo and an oil depot in Kalach-on-the-Don." (AFP/Reuters)