Lviv, Ukraine - Several people were killed and injured in a barrage of Russian missile strikes that damaged dozens of buildings in western Ukraine overnight, officials said on Tuesday.

Air raid alerts were issued across the entirety of Ukraine as 24 cruise missiles were fired by Russian fighter jets flying over the Caspian Sea, the Ukrainian Air Force said.

In addition, a Russian frigate in the Black Sea launched four Kalibr cruise missiles.

Air defenses intercepted 16 of the missiles, the air force said.

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At least three people were killed in the north-western city of Lutsk, located in the Volyn region bordering NATO-member Poland, said regional governor Yuriy Pohulyaiko.

Several injured people were taken to hospitals.

Lviv, the largest city in western Ukraine, and its surrounding area were also hit in the early hours of Tuesday by Russian cruise missiles, Mayor Andriy Sadovyi said.

About 40 buildings were damaged, with the attic of an apartment building catching fire and the grounds of a kindergarten pounded, he said.

The mayor released a video that he said was a deep bomb crater left by the Russian missile that hit the kindergarten's premises.

Rocket impacts were also reported from the cities of Dnipro and Zaporizhzhya, as well as Kramatorsk, which are closer to the front lines in eastern Ukraine.

One man died in Kramatorsk, local prosecutors said.