Russian-backed rebels in eastern Ukraine accused Kyiv government forces of firing artillery and mortars in three incidents on Friday, the Interfax news agency reported.
Kyiv and the rebels blamed each other for escalating tensions after artillery and mortar attacks on Thursday, prompting fears that Russia, which has massed over 100,000 troops near Ukraine's borders, could get involved.
The Kremlin said on Thursday it was "deeply concerned" with the flare-up in Ukraine and was watching the situation closely. The United States said Russia was looking for a pretext for war.
According to the Interfax report, the self-proclaimed Donetsk People's Republic said the shelling targeted the Petrivske village in the breakaway region at 5:30 a.m. (0330 GMT).
Another self-proclaimed rebel republic, Luhansk, reported two incidents of mortar fire on Friday morning.
Kyiv and the pro-Russian separatists have been at war for eight years and the ceasefire between the sides is routinely violated, but the intensity of fighting increased notably this week.
Russia's lower house of parliament voted this week to ask President Vladimir Putin to recognize the two Russian-backed breakaway regions in eastern Ukraine as independent, while the European Union told Moscow not to follow through.