"Russian artillery again hit" the All Saints Skete of the Holy Dormition Sviatogirsk Lavra, Zelensky said on Telegram with a video showing the church in eastern Ukraine ablaze.

He said previous bombardment this week by Russian forces "killed four monks and severely wounded four others" at Sviatogirsk Lavra.

The Ukrainian leader said 300 civilians including 60 children had sought shelter from bombs at the church amid fierce fighting in the Donbas.

Plumes of black smoke and flames rose from the onion-shaped domes of a church structure in an unattributed picture shared on social media by Ukrainian Culture Minister Oleksandr Tkachenko.

The church was "destroyed for the first time in the Soviet era. Afterwards, it was rebuilt. And now it has been set ablaze by the Russian army," Zelensky said.

He also called for "barbaric" Russia to be kicked out of UN cultural agency UNESCO.

The Moscow branch of Ukraine's Orthodox church, which manages the monastery, said earlier the fire broke out "as a result of hostilities".

"The flames completely engulfed the main church of the monastery," it added.

There was no immediate information on the victims, said the church, which recently decided to break with Russia.

Recent battles between Russia and Ukraine have centred on the eastern Lugansk and Donetsk regions after Moscow failed to capture the capital Kyiv early in the invasion.

The Russian defence ministry said its units deployed north of Sviatogirsk were "not fighting" in the area and accused Ukrainian troops of "setting fire" to the site.

The facility is seen as one of the three most sacred sites in Ukraine for Orthodox believers. Before the war, it drew thousands of pilgrims a year.