Pro-Russian separatists attacked Ukrainian military checkpoints and other strategic points in eastern Ukraine overnight but they were beaten off with only minor casualties on the Ukrainian side, a government forces spokesman said on Tuesday.
In a three-hour battle near the airport of Kramatorsk, rebels attacked the army with mortars but government forces returned fire, destroying their position and killing 40 "mercenaries", said the spokesman, Vladyslav Seleznyov.
This figure could not be independently confirmed and there was no immediate word from the side of the separatists.
In Slaviansk, just north of Kramatorsk, two Ukrainian soldiers were wounded when rebels, who control the city, attacked an army position on the perimeter using grenade-launchers.
In Luhansk, on the border with Russia, separatist fighters opened fire on the airport and nearby Ukrainian army positions.
"The attack of the (separatist) fighters was repelled by special force units. There are no losses on the Ukrainian side," said Seleznyov.
Separatist rebellions broke out in Russian-speaking regions of eastern Ukraine in April after street protests in the capital Kiev toppled a Moscow-backed president. Scores of separatists, members of government forces and civilians have been killed.
Kiev has accused Moscow of fomenting the unrest and allowing mercenaries from Russia to cross the long border with consignments of arms to support the rebels. Moscow denies this.
Ukraine's newly-elected pro-Western president, Petro Poroshenko, who took office on Saturday, has pledged to end the fighting while promising to address the legitimate grievances of people in the east, by for example granting them greater autonomy and guaranteeing the status of the Russian language.
Ukraine said on Monday it had reached a "mutual understanding" with Russia on parts of a peace plan proposed by Poroshenko, though it gave no details and Moscow made no direct comment on the issue.
However, the overnight clashes demonstrated the continuing high tensions in the hot spots of eastern Ukraine.
In a separate initiative, Poroshenko ordered security chiefs to establish a "safety corridor" to help civilians caught up in the fighting to leave the area if they wished, his press service said on Tuesday.
Poroshenko also told the government to organize medical assistance to civilians in areas at risk and to send in mobile units to deliver drinking water, food and medical supplies.