The fall of the besieged town of Debaltseve was one of the worst defeats of the war for Ukraine's troops, unable to stop an advance by Moscow-backed rebels fighting for territory the Kremlin calls "New Russia".
Twenty-two Ukrainian soldiers had been killed in the town in the past few days, the Ukrainian military high command said, with more than 150 wounded.
President Petro Poroshenko, who flew to the front-lines, nevertheless tried to cast the battle in a positive light, saying that by holding out as long as they had, Ukraine's troops had exposed "the true face of the bandits and separatists who are supported by Russia".
The Ukrainian troops had held out for three days beyond the start of a Europe-brokered ceasefire, forcing the rebels to disavow the truce to advance on the town.
Eighty percent of the troops had withdrawn from the town by morning, Poroshenko said, and the rest were leaving in what he described as a planned and orderly withdrawal. He said the force withdrawing numbered more than 2,000 men.
A commander of one of the main pro-government volunteer battalions who fought alongside regular Ukrainian forces said "a lot of bodies" had been left behind. The wounded were being taken to Artemivsk about 30 km (18 miles) north of Debaltseve in government-controlled territory.
The rebels described the battle as a victory and said they let the Ukrainian troops leave only after they were defeated.
"There were no attempts by Ukrainian forces to break through. The surrounded Ukrainian forces were completely demoralised. They lost their direction. They began shooting at residential areas of Debaltseve," a senior rebel commander, Eduard Basurin, told journalists.
The rebels say the ceasefire, negotiated by Ukraine, Russia, Germany and France at a summit in Minsk, Belarus, last week, never applied to Debaltseve, which links the two rebel-controlled regions of eastern Ukraine, Donetsk and Luhansk.
Poroshenko and the West say the rebel assault was reinforced by Russian tanks, artillery and soldiers, and that Moscow was behind the decision to disavow the truce and advance. Russia denies supporting the rebels.
PUTIN TELLS KIEV TO SURRENDER
Putin showed no sign of backing down over Ukraine on Tuesday evening when he told Kiev's pro-Western leaders to let their soldiers surrender in Deabltseve to avoid more bloodshed.
Hours later, the Ukrainian withdrawal was under way. A Reuters witness saw weary Ukrainian troops, their faces blackened, some in columns, some in cars, arriving in Artemivsk, about 30 km (20 miles) north of Debaltseve.
A Reuters correspondent near Debaltseve saw black smoke rising over the town and heard loud blasts hours after the withdrawal began.
"One hundred and sixty-seven wounded have been taken to Artemivsk. They did not pick up a lot of bodies. I don't know the total figure," Semen Semenchenko, who heads the Donbass paramilitary battalion, said on Facebook. The rebels said 153 Ukrainian soldiers had given themselves up.
The refusal of the rebels even to pay lip service to halting the advance at Debaltseve puts Western countries in a bind. They need to decide whether to take more steps to punish Russia for violating the ceasefire, or place more emphasis on restoring the truce now that the contested town has fallen.
"The actions by the Russia-backed separatists in Debaltseve are a clear violation of the ceasefire," European Union foreign policy chief Federica Mogherini said in Brussels.
"The EU stands ready to take appropriate action in case the fighting and other negative developments in violation of the Minsk agreements continue," she said, an apparent threat of further economic sanctions.
A German government spokesman said the Minsk agreement had been damaged but it made sense to try to implement it.
Canada imposed sanctions on Russia over its conduct in Ukraine on Tuesday, a move Moscow said would fuel further tension and prevent the implementation of the ceasefire.
NATO Secretary-General Jens Stoltenberg said: "The refusal of the separatists to respect the ceasefire threatens the agreement." Britain said Europe should at least extend its sanctions against Moscow if the ceasefire broke down.
For Poroshenko, the retreat may have saved the lives of thousands of Ukrainian soldiers. Before taking a plane out of Kiev to visit the front-line, he said Ukrainian forces had "really socked it" to the rebels.
"We were able to show to the whole world the real face of the bandit-separatists who are supported by Russia, which was a guarantor and direct participant in the Minsk negotiations," he said.
But another military defeat, coming as Ukraine approaches the first anniversary of the overthrow of the Moscow-backed president Viktor Yanukovich, may be difficult to stomach for a population weary of a long conflict.
Russia has already annexed Ukraine's Crimea Peninsula, and Western countries believe Putin's goal is to establish a "frozen conflict" in eastern Ukraine, gaining permanent leverage over a country of 45 million people seeking integration with Europe.
