Losses in the last 24 hours "as a result of fighting were six servicemen killed and 10 wounded," Volodymyr Polyovy, spokesman for the National Security and Defence Council, said.
Polyovy said the deaths showed that separatist forces "continue to violate the ceasefire agreement" signed September 5.
One of the main attacks took place at the ruins of Donetsk airport, which remains partly in Ukrainian hands, despite lying in territory mostly controled by the separatists, officials said.
Explosions could be heard about every five seconds, accompanied by the sound of machine-guns, AFP correspondents in Donetsk said.
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There was also heavy rebel shelling of Krymske, a village near Lugansk, another major separatist town, the regional governor said.
The bombardments formed a frightening backdrop to elections tomorrow in the self-declared, pro-Russian statelets known as the Donetsk People's Republic and the Lugansk People's Republic.
There were no signs of polling stations in Donetsk near the airport and rebel soldiers deployed there said they didn't know of any stations in the area. However, there was little doubt about the winners of the two polls, with separatist leader Alexander Zakharchenko on course to become head of the Donetsk republic and Igor Plotnitsky in Lugansk.
"These elections are important because they will give legitimacy to our power and give us more distance from Kiev," said Roman Lyagin, election commission chief of the Donetsk People's Republic.