The Russian military claimed Friday to have made advances in the besieged port city of Mariupol, just two days after Ukrainian units blockaded in the city said they had consolidated their defenses.

"The grouping of Russian troops and units of the Donetsk people's militia have completely liberated Ilyich Steelworks from Ukrainian nationalists as a result of the offensive in Mariupol city," Russian military spokesman Maj. Gen. Igor Konashenkov said in a statement on Friday.

CNN cannot independently verify Konashenkov's claim, but the commanders of two Ukrainian units defending Mariupol issued a video statement on Wednesday saying they had been able to consolidate forces inside the city. Denis Prokopenko, the commander of the Azov Regiment, said his unit had linked up with troops from the 36th Marine Brigade, but acknowledged that some Ukrainian defenders had surrendered.

In a statement earlier this week, Ukrainian Marines had vowed to fight on, despite dwindling supplies and ammunition.

The Institute for the Study of War (ISW), an independent think tank that monitors the Russian military campaign in Ukraine, said on Thursday that Russian troops "continued assaults against Ukrainian defenses in southwestern and eastern Mariupol on April 13, though ISW cannot confirm any territorial changes."

"Ukrainian officials admitted on April 14 that Russian forces captured 'some' personnel from Ukraine's 36th Marine Brigade during their breakout from the Ilyich plant to link up with Ukrainian forces in the Azovstal plant in eastern Mariupol on April 13," it added.

Some context: Ukrainian officials have warned of a major humanitarian emergency in Mariupol, saying around 100,000 civilians still require evacuation.

On Thursday, UN Under-Secretary-General for Humanitarian Affairs and Emergency Relief Coordinator Martin Griffiths called on all parties to provide the safe passage of civilians out of Mariupol, following the announcement that two aid workers and their family members were killed there in March.

The military governor of Ukraine's Donetsk region, of which Mariupol is a part, said on Tuesday the situation in the besieged city was "difficult," citing preliminary estimates that as many as 22,000 people had died in the city.

Independent casualty figures from the fighting in the devastated city are not available.