Dozens of volunteers including hospital staff and rescue workers dug through debris from the Okhmatdyt paediatric hospital in a desperate search for survivors after the rare day-time bombardment.
President Volodymyr Zelensky said Russia launched dozens of missiles toward five towns and cities in southern and eastern Ukraine as well as the capital.
Zelensky said at least 37 people were killed, including three children, with more than 170 wounded. 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.
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 promised new measures to boost Ukraine’s air defences.