"Ukraine has lost one servicemen and four more sustained injuries" in the past 24 hours, military spokesman Vladyslav Seleznyov told reporters in the capital Kiev.
The soldier's death brings to 65 the number of troops killed in sporadic clashes along the frontline since the February 12 peace deal was signed, according to the government.
The separatists rarely give accounts of their losses.
Kiev said the latest skirmishes took place near the bombed-out shell of Donetsk airport, which the rebels control, as well as in Shyrokyne, a village near the southeastern port of Mariupol.
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Government positions in both areas had come under fire from 120 mm mortars, which were supposed to have been withdrawn under the truce signed in the Belarus capital Minsk, the army said.
The peace deal calls for the removal of all artillery of a calibre of 100 mm or more.
President Petro Poroshenko confirmed Monday that both sides had withdrawn most of their heavy weapons, yielding a tense calm along much of the 485-kilometre (300-mile) frontline.
The conflict, which has killed over 6,000 people, began 11 months ago when the separatists took up arms against Kiev's pro-Western authorities following the ouster of Moscow-backed president Viktor Yanukovych after months of street protests.