"Over the last day, as a result of hostilities one Ukrainian soldier was killed and another injured," military spokesman Andriy Lysenko told journalists.
The incident occurred during the shelling of Zaitseve village near Gorlivka, some 55 kilometres northeast of the rebels' de facto capital Donetsk, he said.
His death came after officials said two government soldiers and two rebel fighters were killed in fighting on Sunday in the first casualties of the year in the conflict-hit region.
"The situation in Donetsk People's Republic has greatly escalated", the separatist DAN news agency said.
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Over 9,000 people have been killed and more than 20,000 injured in the conflict in Ukraine since April 2014, according to the United Nations.
A shaky ceasefire that started in September has calmed fighting along the frontline but sporadic clashes still occur at key hotspots.
Little progress has been made on a political roadmap deal agreed last February that aims to see Ukraine hold local elections in the rebel-held territory, and for Kiev to resume control of the border with Russia.