Around 30,000 people have fled Mariupol amid the continued Russian attack on the key Ukrainian port city, local authorities announced Thursday, adding that they were "clarifying information on victims" of the shelling of a theater sheltering civilians a day prior.

Mariupol's city hall said on Telegram that "around 30,000 people have left on their transport," adding that 80% of residential housing had been "destroyed." It said it was "clarifying information on victims" of the theater shelling.

On Wednesday, Ukraine accused Russia of bombing a theater in Mariupol where hundreds were taking shelter, despite a sign saying "DETI" – or children in Russian – etched out in the ground on either side of the building.

The city hall said on Thursday that a swimming pool also sheltering civilians – "mostly women, children and the elderly" – had also been shelled.

It said that "an average of 50 to 100 air bombs are dropped on the city per day."

Officials described the situation as "critical," estimating that around 350,000 residents are hiding in shelters and basements in the city.

They added that the Ukrainian army is "continuing to heroically hold the defence of Mariupol and repel enemy attacks" and that troops are fighting "for every street."

The strategic port city on the Azov Sea has been under heavy Russian shelling for days and cut off from food and other vital supplies.

It is only possible to leave the city by private car, with authorities saying that around 6,500 cars left the city in the last two days.

Many struggle to get out amid a communications blackout.

Ukraine says more than 2,000 people have died in Mariupol so far./FP