Several dozen Grad multiple rockets could be heard firing early in the morning from the area of Putilovsky, a Donetsk neighbourhood near the city's ruined airport, AFP correspondents said.
A Ukrainian government-held base nearby in Avdiivka was hit by the heavy rockets, a local resident there told AFP by telephone.
"The shelling began during the night. Everyone was expecting fighting to start right back up after Sunday's elections in Ukraine," said Marina, at a separatist checkpoint in Putilovsky. "It's fine, this is our side shooting. But now there will be the reply from the Ukrainians."
Kiev accuses Russia of arming and organising the rebel militias, charges Moscow denies.