Video released by Ukrainian fighters shows civilians, including children, hiding in a bunker under the Azovstal steel plant.
The plant is thought to be the last Ukrainian stronghold in Mariupol, an official has said.
The video, believed to have been filmed on April 21 by the Azov battalion, shows women and children sheltering underground at the factory.
One boy says "they can go on, but we want to go home and want to see the sun again" and two women say they have been underground since March 5 - seven weeks ago.
Russian troops surround the factory outside and announce safe passage will be guaranteed for those who surrender, but an official said Russian troops resumed attacks on Saturday.
Oleksiy Arestovych, an advisor to the head of Ukraine’s presidential office, said on Saturday that Russian forces are carrying out air strikes on Azovstal and were trying to storm it.
Last week, the city's council said more than 1,000 civilians were sheltering under the plant.
“The enemy is trying to completely suppress resistance of the defenders of Mariupol in the area of Azovstal,” Mr Arestovich said.
"Our defenders are holding on, and despite of their difficult situation, are managing to counter attack."
His claim has not been independently verified, but if confirmed, the attacks would seem to indicate another shift in Russian tactics, as Vladimir Putin called off the military assault on the steel works on Thursday.
His statement came two days after Russian Defence Minister Sergei Shoigu reported to Putin that the whole of Mariupol, with the exception of Azovstal, had been “liberated” by the Russians. Putin ordered the Russian military not to storm the plant and instead to block it off in an apparent attempt to stifle the remaining pocket of resistance there.
The latest satellite images outside of Mariupol appear to show a second mass grave being made during Russia's occupation - the Kremlin has denied trying to cover up the slaughter of civilians.
Despite increased military activity, the Ministry of Defence (MoD) said in its latest intelligence assessment that Russian forces have made no major gains in the last 24 hours.
"Despite their stated conquest of Mariupol, heavy fighting continues to take place, frustrating Russian attempts to capture the city, thus further slowing their desired progress in the Donbas," the MoD tweeted on Saturday.
According to Ukrainian officials, some 1,000 civilians, including women and children, remain trapped at Azovstal, together with the Ukrainian troops holed up there.
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More than 100,000 people- down from a pre-war population of about 430,000- are believed to be trapped in Mariupol, with little food, water or heat, according to Ukrainian authorities.
Officials have been warning for weeks that the humanitarian situation in the besieged city is worsening, with many residents trying to survive without electricity.
With assaults continuing, Ukrainian Deputy Prime Minister Iryna Vereshchuk said "there is a possibility" a humanitarian corridor out of Mariupol could be opened up on Saturday, though assurances of safe passage have been broken before.
She said that “if all goes well” evacuation will begin at noon local time.