"We tentatively decided to postpone the evacuation until tomorrow," the ministry's spokeswoman, Ella Zhuranskaya, said.
In early February, both Kiev and independence supporters started evacuating civilians from Debaltseve. Earlier in the day, Donetsk leader Alexander Zakharchenko ordered that transport was sent to evacuate all the civilians who were still in the town.
Thousands of Kiev troops are reportedly surrounded in the town at the moment. A source in the DPR Defense Ministry told RIA Novosti earlier on Tuesday that some 120 Kiev servicemen had surrendered.
On February 15, a ceasefire between Kiev forces and Donbas pro-independence fighters came into force, however, since then truce violations have been reported.