Fighting was ongoing around Donetsk airport and in Stanitsa Luganska, near rebel-held Lugansk, the spokesman, Andriy Lysenko, told a news briefing.
The town hall of Donetsk, also held by the separatists, said in a statement that powerful explosions were heard early today and that one civilian was killed.
Also today, the pro-Kiev governor of the Lugansk region said two 78-year-old pensioners were killed in eastern Popasna.
Meanwhile a convoy of more than 80 trucks laden with humanitarian aid from Russia was expected in Donetsk after being delayed by snow, a rebel source said.
The conflict between pro-Russian separatists and Kiev solders has raged for more than seven months, claiming at least 4,300 lives according to the United Nations.
Nearly a million people have been displaced.