A nationwide air alert was in place as drones and missiles struck Kyiv, Odesa, Dnipropetrovsk, Kharkiv and Lviv in the early hours of Friday morning.
Ukraine's Air Force spokesperson Yuriy Ihnat said Russia used hypersonic, cruise and ballistic missiles, including X-22 type, which are difficult to intercept.
A metro station that was acting as an air raid shelter was struck, and fires broke out at several warehouses and residential buildings.
Kharkiv mayor Igor Terekhov said one person was killed and several injured in a series of strikes on the city which damaged a hospital and residential buildings.
The Russian attack comes a day after Ukrainian President Volodymyr Zelensky thanked the US for its last approved $250m (£195.7m) military aid package, which included air defence ammunition.
Writing on Telegram, Ukrainian presidential aid Andriy Yermak said "the world needs to see that we need more support and strength to stop this terror".
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