Uncollected corpses wrapped in blankets, coats or any available covering lie in courtyards cleared of debris. Those killed are often buried in common graves.

All around are the blackened shells of the sprawling tower blocks typical of Soviet-era dwellings. Twisted metal on balconies, shattered windows, woods, metal and other wreckage scattered between buildings and in streets.

About 400,000 people have been trapped in the strategic port city on the Sea of Azov for more than two weeks, sheltering from heavy bombardment that has severed central supplies of electricity, heating and water, according to local authorities.

Russia's defence ministry said on Friday its forces were "tightening the noose" around Mariupol and fighting had reached the city centre.

With no running water or heating, women crouch around makeshift barbecues to cook whatever food they can find. As spring approaches, there is no longer any snow to melt for drinking water.

Residents say no one expected this in post-Soviet Ukraine - an unrelenting onslaught from what was once thought of as a "fraternal" Russia - though some have lived through other upheavals that jolted the country back under Soviet rule.

"She had a Russian passport, Russian citizenship, lots of medals," said a downcast Alexander, 57, gesturing toward the place in the open where the body of his wife's mother lies for now.

"My mother-in-law was born in 1936. She survived through the siege of Leningrad," he said, referring to the 900-day Nazi encirclement of the city now known as St Petersburg.

"She was an honoured worker of fish farming in the Russian Federation. So that is where she is."

Officials in Mariupol say 2500 people have died since Russian forces poured across the Ukrainian border on February 24.

Donetsk region governor Pavlo Kyrylenko said about 35,000 had managed to leave the city in recent days during the rare moments when Russian shelling subsides.

Those left occasionally verge on despair - the cold and the anxiety taking their toll.

"I feel terrible. I don't want to blame anyone, but I'm disgusted and scared. And I'm cold," said one woman, Olga, who wore a pink hat under a hoodie and a big coat.

"I just don't have any words. I wasn't ready for my life to become like this."

Russia denies targeting civilians and accuses Kyiv of using them as human shields, something Ukrainian officials deny.

Mariupol is seen as a strategic prize for the Russian invaders to create a bridge between Crimea, annexed by Moscow in 2014, and two separatist enclaves in eastern Ukraine.

A maternity hospital was bombed last week, sending patients fleeing into the street. A theatre used to shelter families forced from their homes was also struck, despite the word "children" being written outside in letters big enough to be read by pilots.

A sense of solidarity among residents fearing for their lives has taken hold. Strangers take in other strangers.

"We spent two days in the basement. She couldn't move. I thought she wouldn't survive," said one middle-aged resident, gesturing to her elderly mother.

"Then we managed to leave the basement. This is the first time I have seen these people. But they sheltered us. And here we are sitting here, covered in blankets. It's very cold here. We just want to go home."

Children, look on, uncomprehending.

"Don't worry, my little darling. Everything will be all right," said one unsmiling young mother, hugging her two school-age children.

In the courtyard, groups of men milled about aimlessly, surveying the shattered buildings.

And around them lay the bodies. The only identifying markers are scraps of paper, appended to makeshift crosses, each bearing a name and a date of birth and death. And no indication when they will be collected.

Australian Associated Press