Fierce fighting is reported inside the key Ukrainian town ofDebaltseve despite a ceasefire deal agreed last week.
Rebels say they have taken most of Debaltseve, a transport hub, but the government says it is still in control.
International observers tasked with monitoring the ceasefire have been unable to enter the town.
Earlier, both sides failed to begin withdrawing heavy weapons, despite a Monday deadline agreed in the truce.
The two sides were given until two days after the latest ceasefire came into effect to start the pullout.
A spokesman for the self-proclaimed Donetsk People's Republic told Russian news agency Interfax that the police station in Debaltseve had been taken as well as the railway station.
He said most of the city was under the control of the separatists and that a mopping-up operation was continuing.
The rebels also said that dozens of Ukrainian troops in Debaltseve had surrendered and others had been killed.
A Ukrainian military spokesman quoted by Reuters news agency confirmed that rebels were attacking the railway station but said the town was still in government hands.
Although Debaltseve has suffered weeks of artillery exchanges, correspondents say this is the first fierce fighting inside the town.
The ceasefire, which came into effect on Sunday, has been broadly observed but separatists insist the agreement does not apply in Debaltseve because they have the town almost surrounded.
Rebels have offered Ukrainian troops under siege there a safe corridor to leave.
Senior rebel leader Denis Pushilin described Debaltseve as "internal territory" and said fighting for it was "a moral thing".
"We do not have the right [to stop fighting]," he told Reuters.
Another rebel leader, Andrei Purgin, said separatists planned to discuss the possible withdrawal of weapons later on Tuesday with representatives of Ukraine, Russia and the OSCE, Russian news agency RIA Novosti reported.
Ukraine's military said on Tuesday that five soldiers had been killed and 14 wounded in the past 24 hours. A spokesman told AFP news agency that most of the deaths happened near Debaltseve.
Meanwhile, the leaders of Germany, Ukraine and Russia discussed the crisis in an overnight phone call.
Germany said they had agreed "concrete measures" for observers to have greater access, but gave no details.
Observers from the Organization for Security and Co-operation in Europe (OSCE), who are charged with monitoring the ceasefire, have been trying to reach Debaltseve after being denied access by pro-Russian rebels on Sunday.
"The German chancellor and Ukrainian president called on the Russian president to exercise his influence on the separatists to enforce the ceasefire," German government spokesman Steffen Seibert said.
"Further, the withdrawal of heavy weapons should be started on Tuesday, as agreed in Minsk."
Under the ceasefire agreed in the Belarus capital Minsk last week, the withdrawal of heavy weapons from front line areas was due to start no later than the second day after the truce came into effect and be completed within two weeks.
The withdrawal would create buffer zones 50-140km (30-85 miles) wide.
But both sides says they will not withdraw heavy weapons until they see movement from the other side.