A rebel official for human rights, Daria Morozova, said an initial exchange of prisoners with the Ukrainian side would take place tomorrow, the Interfax news agency reported.
There was no immediate confirmation from Kiev, but such a swap was agreed by both sides as part of the truce forged last week in the Belarus capital Minsk under European mediation.
That UN-backed truce, though, has been left in tatters by repeated violations since it came into effect last Sunday, with each side regularly accusing the other of ceasefire breaches.
Kiev said 13 troops were killed in the withdrawal. But the rebels, now in control of the town, said they found the bodies of 57 soldiers - as well as many abandoned weapons, including 28 tanks.
Ukrainian President Petro Poroshenko, whose government is being criticised for incompetence over the rout, accused Russia of ordering the Debaltseve offensive and called for international peacekeepers to be deployed.
"This is a critical moment for Ukraine," warned Ivica Dacic, the head of the Organization for Security and Cooperation in Europe (OSCE) which is tasked with monitoring the ceasefire.
In a statement, Dacic urged an immediate halt to hostilities, saying he was "concerned that the continuous breaches of the ceasefire... May lead to uncontrolled violence".
Significantly, there has been no confirmation of either side pulling back heavy weapons from the frontline, which was meant to begin Tuesday and be completed by March 3.