"Over the last day, as a result of clashes one Ukrainian soldier was killed and another three were wounded," military spokesman Oleksandr Motuzyanyk told journalists.
He was killed by mortar fire on the outskirts of Gorlivka, some 30 kilometres northeast of the rebels' de facto capital Donetsk, Motuzyanyk said.
The spokesman said the other Ukrainian soldier was killed when his vehicle hit a makeshift explosive device, which also injured another serviceman.
Kiev and the West have accused Russia of suporting the insurgency and sending regular troops across the border, claims that Moscow has repeatedly denied.
A series of truce agreements have helped to significantly reduce the fighting, although sporadic clashes continue on the frontline.