A Kiev military source said four Ukrainian soldiers had been killed and 21 wounded since the internationally negotiated ceasefire came into force on Sunday.
A Reuters correspondent at Vuhlehirsk, about 10 km (6 miles) to the west of Debaltseve, a government-held railway junction town that has been the focus of most of the fighting in recent weeks, heard heavy shelling, with blasts around every 10 seconds.
The ceasefire was negotiated at a summit of leaders of Ukraine, Russia, Germany and France in Belarus last week in an attempt to end 10 months of conflict in eastern Ukraine in which more than 5,000 people have been killed.
Although fighting generally ceased in the first minutes of Sunday after the ceasefire came into force, military spokesman Anatoly Stelmakh told reporters it had continued, or even escalated, around Debaltseve.
“The illegal armed groups are not supporting the ceasefire,” he said, adding the rebels were using Grad rockets and tanks to attack government forces holding the town.
“The number of attacks on Debaltseve has even increased in comparison to previous days and they are using all types of weapons,” Stelmakh said. “The terrorists have been given the order to take Debaltseve at all cost.”
In all, government positions had been fired on 112 times by rebels in the past 24 hours, with government forces firing only when they came under attack, Stelmakh said.