A unit was attacked near the town of Kramatorsk by about 30 insurgents with heavy weapons, it said. Eight more servicemen were wounded.
Donetsk region is one of two in eastern Ukraine that declared themselves separate from Ukraine after referendums deemed illegal by Kiev, the US and EU.
In Luhansk, separatists said an attempt was made on the life of a rebel leader.
Self-declared governor Valery Bolotov was shot and had lost a lot of blood, but his life was not in danger, the press office of the “Luhansk People’s Republic” said.
Earlier the Kiev-appointed governor of Donetsk region said Ukraine was planning a national referendum on devolving power to regions.
Speaking at a news conference in Donetsk, Serhiy Taruta called on parliament to pass legislation which would authorize a vote to help regions get more power while remaining within Ukraine.
Serhiy Taruta also described Sunday’s separatist referendums in Donetsk and Luhansk as “an opinion poll”.
He said the self-declared “People’s Republic of Donetsk” did not exist legally or politically, and that the Donetsk region could not survive economically as an independent territory.
People in the east “should hear answers to the questions that they are concerned about”, he said.
Separatists in Donetsk and Luhansk say 89% and 96% respectively voted in favor of “self-rule” in the referendums.
Armed rebels remain in control of many official buildings across eastern Ukraine.
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