The explosion of outgoing mortars being fired from near the centre towards government positions at the ruined airport could be heard from early in the morning, setting off car alarms, an AFP journalist said.
Donetsk's city hall said in a statement that "the sound of artillery fire and explosions can be heard in all districts" of the mining hub.
The intensified shelling, the heaviest heard since the weekend, comes after monitors from the Organization for Security and Cooperation in Europe (OSCE) in east Ukraine warned that growing clashes could tip the region back into all-out conflict despite a frequently-violated ceasefire deal.
Ukraine's military said that one soldier had been killed and two wounded as it positions came under repeated shelling around the region.
Government forces also accused the rebels of trying to capture a strategic location along the volatile frontline, delineated as part of the ceasefire deal, north of the second-largest rebel city Lugansk.