DEBALTSEVE, Ukraine — Outgoing heavy-caliber fire boomed incessantly, shaking the ground and rattling windows around the besieged town. Residents of Debaltseve, seemingly inured to the racket, listened impassively as they mustered at the town hall on Saturday to be evacuated with as many belongings as they could carry.

The government-held town has been without power, water and gas for at least 10 days, prompting many to flee from an intense artillery duel between government and Russian-backed separatist forces. Almost every one of the largely deserted streets in the center showed signs of having been struck by projectiles.

A month of relative quiet in eastern Ukraine was shattered in early January by full-blown fighting as the separatists attempted to claw back additional territory from government hands. Rebel leaders accused Ukraine of mobilizing its forces in advance of an imminent offensive.

Ukrainian Prime Minister Arseniy Yatsenyuk said on Saturday that 1,000 residents have been evacuated in the past days from Debaltseve. But the number of crammed civilian vehicles seen speeding out of the town’s rutted, icy roads over the past few days suggests official figures may be on the conservative side.

“Six buses shuttle (refugees) from there and they constantly come under fire,” Yatsenyuk said in comments carried by his press office. “As soon as they (the rebels) see that we are evacuating the people, they open fire.”

Yatsenyuk has asked the defense ministry to help secure the evacuation and added that none of the refugees has been injured.

Vyacheslav Abroskin, head of police for the Donetsk region, said 12 people had been killed by shelling in Debaltseve, which hosts a strategic railway hub. He did not specify over what period the deaths had taken place.

With the government apparently unable to handle all the people wishing to leave, volunteer groups are trying to fill the gap.

“We are evacuating people from this hotspot, so they don’t have to deal with what is going on, because this is not their war after all. This has nothing to do with them,” said Andrei Vasilyev, a worker with a charitable organization based in the eastern city of Kharkiv.

As Vasilyev’s minibus was being loaded, a small child held in her mother’s arms cried and pleaded plaintively to leave as soon as possible. Infirm and elderly passengers needed to be lifted into the tightly packed transport.

Leaving Debaltseve carries its own risks because of the encroachment of separatist forces on all sides. Roads running west and east are controlled by rebels, leaving the northbound road the only remaining corridor of relative safety. But fresh, scorched shell craters alongside that road testify that it is dangerous too.

Fighting inched toward Debaltseve this week when separatists burst through government lines to occupy part of the town of Vuhlehirsk.