As many as 300 people may have been killed in the bombing of a theatre in the besieged city of Mariupol, according to Ukrainian authorities.

Local officials citing witness accounts said up to 300 people are feared dead after a drama theatre where hundreds of people had been sheltering was struck by a powerful Russian air strike on March 16.

"From witnesses comes information that about 300 people died in the Mariupol Drama Theatre as a result of the bombing by a Russian plane," Mariupol city council said in a statement on Friday.

Ukrainian officials previously said about 130 people were rescued from the rubble and that the theatre basement, where many people were reportedly sheltering at the time of the bombardment, had withstood the attack.

The Ukrainian government said it was impossible to get an exact death toll because Mariupol was under almost constant bombardment from Russian forces.

Russia has denied bombing the theatre.

Attempts to arrange passage out of Mariupol

Meanwhile, Ukrainian authorities are hoping some civilians who have been trapped in Mariupol will be able to leave in private cars on Friday.

Repeated attempts to arrange safe passage out of the southern port city, which is surrounded by Russian forces, have failed.

Civilians trapped there have been sheltering in basements with little food, power or running water.

Those who manage to leave Mariupol will find buses awaiting in the nearby city of Berdyansk which will take them to the city of Zaporizhzhia, Deputy Prime Minister Iryna Vereshchuk said.

Efforts to evacuate as many residents as possible came as the death toll continued to rise, with reports of mass graves being dug to bury victims.

The head of the UN human rights team in Ukraine said monitors had received increasing information about mass graves, including one that appeared to hold 200 bodies.

"We have got increasing information on mass graves that are there," Matilda Bogner told journalists by video link from Ukraine, saying some of the evidence came from satellite images.

Ms Bogner said civilian deaths in Ukraine exceeded 1,035, adding that the UN team was probing what appeared to be indiscriminate attacks by both sides in the conflict.

Ukrainian troops take back eastern towns

Ukrainian troops are recapturing towns east of the capital Kyiv, and Russian forces who had been trying to seize the city are falling back on their overextended supply lines, according to British intelligence. 

Battlelines around Kyiv have been all but frozen for weeks with Russian columns threatening Kyiv from the north-west and the east.

But in an intelligence update on Friday, Britain described a Ukrainian counter-offensive that had pushed the Russians far back.

"Ukrainian counter-attacks, and Russian forces falling back on overextended supply lines, has allowed Ukraine to reoccupy towns and defensive positions up to 35 kilometres east of Kyiv," the update said.

It said Ukrainian forces were also likely to try to push the Russians back on the other main axis threatening Kyiv from the north-west, while in the south, Russia could still be planning to attack the port of Odesa after abandoning efforts to take Mykolaiv.

Meanwhile, Volodymyr Borysenko, mayor of Boryspol, an eastern suburb where Kyiv's main airport is located, said 20,000 civilians had left the area, answering a call to clear out so Ukrainian troops could push the Russians further back.

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Reuters