"We have lost two soldiers in fighting and acts of provocation, five have been wounded," Ukraine army spokesman Andriy Lysenko told reporters.
He accused rebels of using "on 10 occasions artillery over 100 mm calibre." Such heavy weaponry was to have been withdrawn from the front line under the terms of a peace deal signed in Minsk.
The military spokesman said firing came from the area around Donetsk airport, controlled by rebels since January but still a flash point, as well as close to the village of Trokhizbenka in the rebels' self-proclaimed people's republic of Lugansk.
The separatists on their part accused the Ukrainian army of "mass firing" on the city of Donetsk's Kievsky district, close to the airport.
The Ukrainian army said the rebels had fired 152 mm calibre shells close to the village of Starohnativka, 40 kilometres northeast of the strategic Azov Sea port of Mariupol, the last major town in the region to be controlled by the Ukraine government.
More than 6,500 people, most of them civilians, have been killed in the conflict, which began in April 2014.