The Ukrainian president says his forces are making an "organised"withdrawal from the embattled town of Debaltseve.
Petro Poroshenko said 80% of Ukraine's troops left on Wednesday morning after several days of fierce fighting.
Russia said Ukrainian forces had tried to fight their way out of the city after being encircled but Mr Poroshenko insisted they were never surrounded.
The rebel advance on Debaltseve, which came in spite of the recent ceasefire agreement, has been widely condemned.
Nato chief Jens Stoltenberg said the rebels' offensive had put the wider peace agreement at risk and urged Russia to "use all its influence on the separatists to make them respect the ceasefire".
He also called on Moscow to withdraw its forces from Ukraine, saying Russian troops, artillery and air defence units were still active in the country.
Earlier, Russian Foreign Minister Sergei Lavrov insisted the rebels' actions in Debaltseve had not violated the ceasefire because it was a rebel-held city when the peace agreement was signed last week.
He urged rebels to provide troops who surrendered with food and clothes and said he hoped the situation in the city would "not be used to find a pretext to actually undermine [the agreement]".
Eyewitnesses saw dozens of tanks and columns of weary Ukrainian troops retreating from Debaltseve on Wednesday.
Russia's state-controlled Channel One TV showed footage of what it said were rebels raising their flag on top of a high-rise building in the city.
One rebel commander in Debaltseve told the BBC that conditions were dire, with no electricity and a shortage of food and water. He said rebels were sharing their rations with the remaining civilians.