Military spokesman Andriy Lysenko said three servicemen were also wounded in rebel artillery and sniper fire across the separatist Lugansk and Donetsk provinces.
Lysenko said the situation remained "very tense" around the industrial Sea of Azov port of Mariupol that the rebels are believed to covet as a potential export gateway for the steel and coal mines they now control.
The violence has pushed to nearly 60 the number of Ukrainian soldiers and civilians killed this month.
The separatists have called government forces' own shelling of the rebel bastion of Donetsk a "grave" violation of Minsk agreement that Russia and Ukraine signed during February negotiations spearheaded by the leaders of Germany and France.