Rebel military spokesman Eduard Basurin was quoted as saying they will take the “initiative” and pull back on some parts of the front line.
This does not appear to include the railway hub of Debaltseve, the epicentre of fighting in recent days.
Russian-backed separatists said earlier yesterday that they had gained control of Debaltseve.
The Donetsk News Agency, a rebel mouthpiece, quoted the separatists as saying their forces had pushed government troops out of Debaltseve and controlled a large part of it.
Fierce fighting yesterday appeared to be focused on the city, which both sides claim is on their side of the ceasefire line.
Ukrainian military spokesmen said at least five troops had been killed and nine injured in the past 24 hours in the war zone as separatists continued to attack government positions, and that the pullout hinged on the ceasefire being fully observed.
“As soon as the militants cease fire, the Ukrainian side will begin to withdraw heavy weaponry from the front line,” he said.
The war in eastern Ukraine has already killed more than 5,600 people and displaced more than a million, according to UN figures. It has also left the country’s industrial heartland in ruins.
The Ukrainian presidential office later called on the European Union and Nato to condemn the rebels for violating the ceasefire.