Russian Defense Ministry spokesman Maj.-Gen. Igor Konashenkov said 1,026 troops from the Ukrainian 36th Marine Brigade surrendered at a metals plant in the city.
Russian forces moved on Mariupol in late February and units in the city have been running low on supplies.
Konashenkov said that the 1,026 Ukrainian marines included 162 officers and 47 female personnel, and that 151 wounded received medical treatment.
Ukrainian presidential advisor Oleksiy Arestovych did not comment on the alleged mass surrender, but said in a post on Twitter that elements of the 36th Marine Brigade had managed to link up with other Ukrainian forces in the city as a result of a “risky maneuver.”
If the Russians seize the Azovstal industrial district, where the marines have been holed up, they would be in full control of Mariupol, the lynchpin between Russian-held areas to the west and east providing a land corridor for troops and supplies.
It would be the first major city to fall to Russian forces since they invaded Ukraine on Feb. 24.
Ukraine’s general staff said that Russian forces were proceeding with attacks on Azovstal and the port.
Reuters journalists accompanying Russian-backed separatists saw flames billowing from the Azovstal district on Tuesday.
Thousands are believed to have been killed under a near-seven week siege of Mariupol and Russia has been massing thousands of troops in the area for a new assault, Ukrainian President Volodymyr Zelenskyy said.