Doug Stanglin, and Jane Onyanga-Omara

USA TODAY

A lengthy convoy of ambulances and green buses rolled out of eastern Aleppo on Thursday in the long-awaited evacuation of anti-government rebels and families from the opposition's last foothold in the war-ravaged Syrian city. Syrian President Bashar Assad said the defeat of the insurgents means "history is being made."

The pullout, marking the end of the opposition's four-year control of eastern Aleppo, had been scheduled for Wednesday, but was scrapped after an earlier cease-fire deal fell through.

A World Health Organization official in Syria helping monitor and carry out the evacuation said it’s “going smoothly.”

By late Thursday night, thousands had left - but tens of thousands remained. The International Committee of the Red Cross told the BBC that aid workers wanted to keep the momentum going and that more than 3,000 people were bussed out on the first day of the evacuation. The UN, however, said that as many as 50,000 are still trapped there.

The surrender by rebels comes after weeks of pounding in the area by Russian-backed Syrian forces on the ground and by air that killed fighters and civilians alike and shrank the opposition fighters' rubble-strewn enclave in the city. Hundreds of civilians have been killed and tens of thousands displaced in the campaign by Assad's government to retake what was once Syria's most populous city.

In Washington, Secretary of State John Kerry charged that Syria, backed by its Russian and Iranian allies, was deliberately targeting civilians in and around Aleppo, despite the evacuation process.

He said there is "absolutely no justification whatsoever" for the "savage brutality against civilians shown by the regime and its Russian and Iranian allies for the past few weeks, or indeed the past five years."

Kerry called for safe passage corridors for evacuees and full access to humanitarian supplies throughout the country. "The killing and suffering could stop, very, very quickly, if Russia and the regime made the decision to do so," he said.

The Britain-based Syrian Observatory for Human Rights said the fighting stopped in the city around 4 a.m. Thursday.​ The group said pro-government forces shot at ambulances trying to leave eastern Aleppo earlier, wounding at least three people.

Syrian state TV broadcast footage showing the withdrawal by rebels and families who were taken aboard municipal buses toward the agreed-on evacuation point inside the opposition-held area. In a video message posted on the Syrian presidency’s Telegram channel Thursday, Assad said that “what is happening is bigger than congratulations.”

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The Russian military, which supports the Assad regime, said the government in Damascus gave security guarantees to all rebels willing to leave Aleppo, and the Russians were monitoring the situation using drones.

Kerry said all international parties backed a ceasefire and negotiations for a political solution through power-sharing to end the civil war.

"The only remaining question is whether the Syrian regime with Russian support is willing to go to Geneva and is prepared to negotiate and constructively end this slaughter of their own people," he said.

Kerry said what he feared now is that the shrinking enclave in Aleppo could turn into a "Srebrenica," a reference to the 1995 genocide of more than 8,000 mostly Muslim residents of that Bosnian town during the Bosnian war.

"If Aleppo falls completely and people are slaughtered in that small area, it will be even harder to bring people around and it will not end the war," he said.

At U.N. headquarters in New York, Deputy Secretary-General Jan Eliasson told reporters that with government troops taking over the rebel-held eastern Aleppo, it is time “to go back to basics.”

Eliasson said Syria and its allies, Russia and Iran, should return to the political track in order to end the “enormous suffering” and destabilization of the region, with its “huge international impact.”

“I hope everybody leans back and looks at the tragedy, the horrors that have fallen on Aleppo, and then really ask themselves: Isn’t this the moment now to go for the full cessation of hostilities and humanitarian access and political transition?” he said.

The pullout continued despite reports from Geneva that broader ceasefire talks between the U.S. and Russia had been suspended.

Russian Deputy Foreign Minister Sergey Ryabkov told the state-owned TASS news agency that "some behind-the-scenes players in Washington, who apparently represent various administration divisions, immediately stepped in to adjust things, to put it mildly, and, to put it straight, to fight back, to retreat to the initial positions, to bring the entire situation back to level one, using the terms of computer games."