Images released by the Ukrainians but not independently verified show their troops pinning down a group of Russian soldiers and tossing grenades over a brick wall. Some Russians wriggle away from the blasts while others lie motionless.
“The defence of Mariupol continues. Despite the overwhelming forces of the enemy, the Azov Regiment fighters launch [a] counter-attack,” an account linked to the battalion said on Twitter.
Justin Crump, a military expert at security consultancy Sybilline, told the BBC there could be 500 to 800 Ukrainian troops holding out in the city.
“It [the steelworks] has nuclear bunkers, tunnels, it’s built to survive a nuclear conflict – they are really well set for defence,” he said. “They have had more than 50 days to fortify it and build escape routes.
“I suspect that unless they are wiped out they’ll be there a long time. It’s credible there would be guerrilla resistance.”
For Russia, the capture of Mariupol is seen as a key step in preparations for any eastern assault because it would free Russian troops up for that new campaign.
The fall of the city, on the Sea of Azov, would also hand Russia its biggest victory of the war, giving it full control of a land corridor to the Crimean Peninsula, which it seized in 2014, and depriving Ukraine of a major port and its industrial assets.
On Monday, the UK Ministry of Defence said in an intelligence update: “Russian commanders will be concerned by the time it is taking to subdue Mariupol. Concerted Ukrainian resistance has severely tested Russian forces and diverted men and materiel, slowing Russia’s advance elsewhere.
“The effort to capture Mariupol has come at significant cost to its residents. Large areas of infrastructure have been destroyed, whilst the population has suffered significant casualties.
“The targeting of populated areas within Mariupol aligns with Russia’s approach to Chechnya in 1999 and Syria in 2016. This is despite the Feb 24 claims of Russia’s defence ministry that Russia would neither strike cities nor threaten the Ukrainian population.”
