A Russian missile destroyed an apartment building and damaged seven more in the eastern Ukrainian city of Kramatorsk on Wednesday night, killing at least three people and injuring 20, regional police said.

Local authorities initially said Russia had fired a rocket but the police force later said an Iskander-K tactical missile had struck at 9.45 pm local time (1945 GMT).

"At least eight apartment buildings were damaged. One of them was completely destroyed," police said in a Facebook post. "People may remain under the rubble."

At least 44 people were killed last month when a Russian missile hit an apartment building in the eastern city of Dnipro.

"This is not a replay of the past, it is the daily reality of our country - a country with absolute evil on its borders," President Volodymyr Zelenskiy wrote on Telegram messaging app.

In a separate tweet, Zelenskiy wrote: "The only way to stop Russian terrorism is to defeat it. By tanks. Fighter jets. Long-range missiles."

Ukraine, which last week secured promises of battle tanks, wants allies to supply fighters and missiles.

Regional governor Pavlo Kyrylenko posted a picture showing a four-story Kramatorsk building that had suffered major damage.

Radio Free Europe's Ukrainian outlet published a brief video clip which showed rescuers working under floodlights as snow fell on the rubble.

Ukraine accuses Russian forces of indiscriminately shelling civilian infrastructure, a charge Moscow routinely rejects.

Last April, Ukraine said 57 people died when a Russian missile hit the train station in Kramatorsk. Moscow denied responsibility, saying the missile was Ukrainian.