Twenty-seven were wounded in the fighting, said Andrey Lysenko, spokesman of the center, at his press briefing.
In a separate incident, three civilians were killed and five injured in shelling overnight in Donetsk, the website of the city office said Monday.
Residential and administrative buildings were damaged as a result of artillery fire, according to the site, which described the situation as tense.
Ukrainian government forces have been fighting pro-Russian separatists in eastern Ukraine for months.
Despite the ongoing violence in places such as Donetsk, Ukrainian President Petro Poroshenko insisted last week that a ceasefire signed with rebel leaders more than three weeks ago was holding.