Residents said the rebels, who want independence from Kiev for Ukraine's Donbass region, had dug trenches in downtown Donetsk outside the main university, where they have been living in student dormitories.
Ukrainian forces have forced the rebels back to their two main strongholds of Donetsk and Luhansk, taking villages and suburbs around them to try to squeeze them out.
"In Donetsk, rebels abandoned their positions en masse and went towards the central part of the city," the headquarters of what Kiev calls its "anti-terrorist operation" said in a statement.
"It cannot be ruled out that the appearance of such movements could suggest the spread of panic and attempts to leave the place of warfare."
Residents said they had heard shelling during the night and a shell struck a chemical plant in the city, causing a fire.
Fighting was also reported in Luhansk overnight, officials in Kiev said.
(Reporting by Elizabeth Piper, editing by Timothy Heritage)