Ukrainian forces still holding out in the eastern city of Severodonetsk are outnumbered by Russian forces, President Volodymyr Zelensky has said.
Both sides fought for the city in street-by-street battles on Monday as artillery shells rained from above.
The intensity of fighting there and in nearby Lysychansk has made them both "dead cities", Mr Zelensky said.
If captured, the two strategic targets would deliver Russian forces the entire Luhansk region in Ukraine's east.
Since pulling its forces back from the Kyiv region in March, Russia has refocused its military efforts on Ukraine's eastern Donbas making slow advances there in recent weeks.
Despite the Russians' superior numbers, Mr Zelensky said the Ukrainian defenders were holding out and had "every chance" of fighting back.
Artillery strikes have also intensified on neighbouring Lysychansk, which Mr Zelensky said he had visited on Sunday as part of a tour of the eastern front line.
An elderly resident in the city, Oleksandr Lyakhovets, said a Russian missile had struck his flat soon after, engulfing it in flames.
"They shoot here endlessly... It's a horror show," the 67-year-old told AFP news agency.
Russian forces have made slow progress in Ukraine's eastern Donbas in recent weeks.
Their troops currently control almost all of the Luhansk region as well as a significant proportion of the neighbouring Donetsk region. The two regions make up the Donbas.
Fighting has been slow and bloody with both sides sustaining significant losses.
Russian state media said on Sunday that one of the army's top officials, Maj Gen Roman Kutuzov, had been killed while leading an offensive on an unspecified Ukrainian town in the region.
Western countries have responded to the grinding conflict with pledges to send even more advanced, long-range weapons to Kyiv that they hope will bolster Ukraine's defensive capacity in the east.
On Monday the UK confirmed that long-range missile systems would be included for the first time in the next batch of military aid that it is sending to Ukraine.
Russian President Vladimir Putin has said he considers any delivery of long-range weapons by Western countries to be a deliberate attempt to prolong the conflict. He said Russia would respond by expanding the list of targets that it was striking across Ukraine if longer-range weapons were sent to his adversaries.
In Mariupol, which was captured by Russia in May after a months-long siege, the Associated Press news agency is reporting that dozens of corpses belonging to soldiers who had been defending the city's Azovstal steel mill had finally been returned to Kyiv where they were undergoing DNA tests.
Other soldiers who survived the siege were taken to Russian-controlled areas. On Monday, Mr Zelensky said that more than 2,500 of them were being held as prisoners of war.
Residents in the now Russian-controlled port city have been facing a growing humanitarian crisis, compounded by severe shortages of food and water.
On Monday a Ukrainian official said contamination from decomposing corpses and rubbish had sparked a cholera outbreak - prompting a city-wide quarantine.
"We are seeing the city get closed off," said Petro Andryushchenko, who is an adviser to the city's mayor, to United News TV.
"The word 'cholera' is being mentioned inside the city, among occupying authorities and their handlers," he added.
The BBC has not been able to independently verify this claim.