Col. Andriy Lysenko told journalists in a briefing in Kiev on Monday that at least nine servicemen had been killed in the last day and 27 had been wounded.
The city council of Donetsk said in a statement published online that at least three civilians were killed and five wounded in overnight shelling of a residential area in the north, where fighting has centred on the government-held airport.
Violence has continued despite a ceasefire declared on Sept. 5. Ukrainian President Petro Poroshenko has been at pains to prove to a skeptical audience at home that his peace plan is working.
Since fighting began in April, the conflict has claimed at least 3,500 lives.
Last week, representatives of Russia, Ukraine, and the rebels signed another agreement that would require both sides to remove all heavy artillery from the front line, creating a buffer zone that would allow the cease-fire to be better enforced.
On Sunday, in the second-largest Ukrainian city, Kharkiv, nationalists tore down an enormous statue of Vladimir Lenin to cheers from the crowd.
Across Ukraine, people have torn down statues to the former Communist leader in a symbolic display of anti-Russian sentiment.
The authorities in Kharkiv supported the move.
Arsen Avakov, Ukraine's Minister of Internal Affairs and a Kharkiv native, wrote on his Facebook page:
"Lenin? Let him fall ... As long as nobody gets hurt."