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.
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"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.
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.