Ukraine’s military has pounded the main pro-Russian rebel stronghold of Donetsk with artillery fire, damaging buildings but few casualties are reported.
A military spokesman said the rebels were in “panic and chaos” and had begun to desert en masse.
Ukraine is mulling the possibility of allowing a humanitarian mission into the area, as residents struggle without power or reliable sources of food.
Some 1,500 people are estimated to have died since the conflict began in April.
Rebels sparked the four-month battle when they overran large swathes of the east and declared independence from Ukraine.
Hardship and fear
The rebels have sent out mixed signals in recent days, calling for a ceasefire but also insisting they would carry on fighting until the army laid down its weapons.
Russia, which is widely accused of providing military support to the rebels, has repeatedly offered to send a humanitarian mission.
Russian media quote Foreign Minister Sergei Lavrov as saying he is in talks with the Ukrainian government, the Red Cross and the UN about an aid mission.
Western powers had expressed fears that Russia would use a humanitarian mission as a pretext to send in troops.
Ukrainian President Petro Poroshenko said late on Saturday he would consider an aid mission, but only if it was international and unarmed.
Donetsk residents are living under increasing hardship, many taking refuge in basements and bomb shelters.
“This is a real war: it’s impossible to live in this city. I’ve been sleeping in the basement for the past week,” Inna Drobyshevskaya, a 48-year-old lawyer, told the Associated Press.
The AP reported constant shelling on Sunday morning.
Buses were still burning on the streets on Sunday after apparently being hit in firefights.
Residential buildings were also badly damaged, according to AP.
Military spokesman Oleksiy Dmytrashkivsky said a number of strikes on enemy positions had been carried out overnight.
“A large number of enemy hardware and personnel was destroyed. Panic and chaos have been noted among the terrorists,” he said.
Some 300,000 people have already fled the city, which had a population of one million before the conflict began.
In the other rebel stronghold of Luhansk, residents have been without power for a week and are struggling to find reliable sources of food.
Reports on Saturday claimed the army had recaptured Krasnyi Luch, a city on the main road between the two cities.
The city’s recapture would in effect divide the two rebel strongholds and allow the army to further squeeze Donetsk.