The news came the same day Russian President Vladimir Putin and German Chancellor Angela Merkel were set to meet in Russia to discuss the long-running conflict.
A 13 year-old boy and his father were killed when their house was hit by shelling in Troitsky, inside a Kiev-controlled zone in the region of Lugansk, local police said.
The boy's mother is in intensive care after she was seriously injured and her other 18-year-old son suffered leg injuries that are not life threatening, the regional governor Yury Garbuz wrote on Facebook.
Rebel authorities reported two of their fighters were killed and a third wounded in the clashes with the Ukrainian army.
Three civilians in Gorlivka, a city in the separatist-controlled Donetsk region, were also wounded, they said.
For its part the Ukrainian army reported seven wounded soldiers.
The situation in eastern Ukraine deteriorated in recent days with two Ukrainian soldiers killed in fighting on Thursday. A school was also hit by shelling this week, despite the ceasefire.
The chief monitor of the Organisation for Security and Co-operation in Europe (OSCE) special mission to Ukraine Alexander Hug left the conflict zone on Thursday due to a "serious deterioration of the security situation", the organisation said.
More than 10,000 people have been killed since the Moscow-backed insurgency broke out in April 2014 following Russia's annexation of Crimea from Ukraine.
Ukraine and its Western allies accuse Russia of funnelling troops and arms across the border to fan the flames of the conflict.
Moscow has denied the allegations despite overwhelming evidence that it has been involved in the fighting and its explicit political support for the rebels.
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