A bomb shelter under a theatre in the besieged city of Mariupol withstood what Ukraine said was a Russian air strike and there are believed to be survivors trapped underneath, an official at the mayor's office said on Thursday.

Ukraine accused Russian forces on Wednesday of dropping a powerful bomb on the theatre, where it says hundreds of civilians including many children were sheltering during a more than two-week-long siege of the encircled port city.

Russia has denied bombing the theatre.

"The bomb shelter held. Now the rubble is being cleared. There are survivors. We don't know about the (number of ) victims yet," mayoral adviser Petro Andrushchenko told Reuters by phone.

He said rescue work was under way to reach survivors and establish the number of casualties, which was still unknown.

Russian foreign ministry spokeswoman Maria Zakharova said on Thursday that the allegation that Russia had bombed the theatre was a "lie".

She repeated Kremlin denials that Russian forces have targeted civilian areas since the Feb. 24 invasion of Ukraine.

"Russia's armed forces don't bomb towns and cities," she told in a briefing.