One soldier died on the spot after the incident near the village of Pisky, with the other victim dying from his injuries soon afterwards, army spokesman Oleksandre Motouzianyk said.
He added that eight troops were hurt with one soldier injured in a separate incident in a different zone.
Kiev accuses separatists of having violated a ceasefire on nine occasions, while the separatists accuse Ukraine of bombarding terrain under their control, according to rebel news agency DAN.
The conflict, which erupted in 2014, has left more than 13,000 dead and driven some 1.5 million people from their homes.
Although a 2015 peace deal ramped down the violence, politically an impasse remains with Kiev accusing Moscow of aiding the rebels -- which Russia denies.
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