Defense Minister Stepan Poltorak said separatists were keeping up intense pressure on Debaltseve, a major rail and road junction north-east of the big city of Donetsk, as well as on the neighboring town of Vuhlehirsk.
"The toughest situation is in the Vuhlehirsk area where the terrorists are trying to seize the town and occupy positions to move forward and encircle Debaltseve," military spokesman Andriy Lysenko said in a separate briefing.
The rebels were also continuing to threaten Mariupol, a town of half a million in the south-east of the country on the coast of Sea of Azov, Lysenko said.
"Along all the lines of conflict our losses amount to 15 killed and 30 wounded," Poltorak told reporters.
The renewed violence followed intense fighting on Friday in which more than 20 civilians were killed in separate shelling attacks in Donetsk, Debaltseve and other areas, Reuters reported.
Rebel delegates meanwhile arrived in the Belarussian capital of Minsk for a new attempt to reopen peace talks with Ukrainian and Russian representatives under the auspices of the Organisation for Security and Cooperation in Europe.
The meeting of the so-called contact group was originally planned to take place on Friday but was called off before it started and there was no certainty the talks would take place on Saturday either.