The evacuation of Syrian civilians and rebels from eastern Aleppo is continuing round the clock, as a truce was reported to be holding overnight.

The International Committee of the Red Cross told the BBC aid workers wanted to keep the momentum going.

More than 3,000 people were bussed out on the first day of the evacuation on Thursday, but the UN says as many as 50,000 are still trapped there.

Syria's army, backed by Russia, has taken nearly all rebel-held districts.

The US accused the Syrian government of carrying out "nothing short of a massacre" in the city.

"The only remaining question is whether the Syrian regime, with Russia's support, is willing to go to Geneva prepared to negotiate constructively, and whether or not they're willing to stop this slaughter of their own people," US Secretary of State John Kerry said.

Syria and Russia have repeatedly denied targeting civilians.

Syrian President Bashar al-Assad on Thursday hailed the "liberation" of Aleppo after more than four years of fighting, saying that history was being made.

Many thousands of people, including a large number of civilians, have been killed during the fierce fighting.

On Friday, ICRC spokesman Pawel Krzysiek told the BBC that "the evacuation is ongoing right now".

"That means we're expected to work around the clock - Syrian Red Crescent volunteers, the ICRC staff. We definitely want to keep this momentum going as the situation of the people is truly desperate there," he added.

The ICRC said earlier that some 3,000 civilians and more than 40 wounded, including children, were evacuated in two convoys on Thursday.

The UN envoy to Syria, Staffan de Mistura, later gave an estimate of the numbers still trapped in eastern Aleppo.

"There are 50,000 people, including 40,000 civilians, unfortunate enough to live in that part of the city."

In other developments on Thursday:

• US President-elect Donald Trump reiterated he would establish safe zones in Syria, which would be partly financed by the Gulf states
• At an EU summit, German Chancellor Angela Merkel described the situation in Aleppo as "heart-breaking" and regretted European diplomacy had failed
• EU Council President Donald Tusk demanded the immediate opening of humanitarian corridors to allow aid into Aleppo
• Britain said it would provide a further £20m ($25m) in aid, including clean water and food, to millions of Syrians

Analysis by Barbara Plett Usher, BBC News, Washington

John Kerry expressed moral outrage at the fate of Aleppo and he stressed that the Syrian regime was responsible for the failure of a year's worth of US-Russian negotiations aimed at a nationwide ceasefire and peace talks.

But he didn't offer any new plan to end the conflict. Nor did he accept that the fall of Aleppo was also due to a failure of US diplomatic strategy. "You can't make someone do something through diplomacy that they're not prepared to negotiate," he told me.

Critics in Washington, though, have slammed the Obama administration for refusing to back that diplomacy with the threat of credible force, giving Mr Kerry very little to work with other than good faith.

Some have faulted the secretary of state for having too much faith in Russia's willingness for a deal - "delusional diplomacy", the Washington Post called it.

Mr Kerry made clear he would continue his tireless efforts to reach a peace deal. But the fall of Aleppo almost certainly means he has run out of time to do so in the waning weeks of this administration, and the Syria crisis will be passed on to the next one.

Syrian state media said rebels had blown up their ammunition dumps and destroyed documents before leaving the city.

The Russian Centre for the Reconciliation of Opposing Sides in Syria, part of Russia's ministry of defence, said the Syrian authorities had guaranteed the safety of all members of the armed groups who decided to leave Aleppo.

As operations began, an ambulance service official in eastern Aleppo said that one convoy of ambulances had been shot at, with three people injured.

Where are the evacuees being taken?

The evacuees were transferred to rebel-held areas in neighbouring Idlib province.

Most of Idlib is controlled by a powerful rebel alliance that includes the jihadist group Jabhat Fateh al-Sham.

The buses left Aleppo via the road through the government-controlled south-western district of Ramousseh, heading towards the nearby rebel-held towns of Khan Touman and Khan al-Asal.

The chief of the Russian military's General Staff, Gen Valery Gerasimov, told a news briefing: "A humanitarian corridor has been created for the evacuation of militants."

"This corridor is 21km (13 miles) long," he said, adding, "6km lie across Aleppo's territories controlled by government troops and another 15km through territories in the hands of illegal armed groups."

But Mr de Mistura has warned that the evacuees could face a more violence in Idlib.

"If there is no political agreement and a ceasefire, Idlib will become the next Aleppo," he said.

Turkey, which helped to broker the evacuation, is preparing to receive some of the most vulnerable civilians.

What will the government do next?

In October, President Assad said victory in Aleppo would be "the springboard... to liberate other areas from terrorists", a term the government uses to describe all rebel fighters.

He singled out Idlib province, west of Aleppo, that is almost entirely controlled by an alliance of Islamist rebel factions and Jabhat Fateh al-Sham, formerly known as al-Nusra Front.

Idlib contains border crossings used by rebels to receive supplies from Turkey, a key backer. It also borders the coastal province of Latakia, the heartland of Mr Assad's minority Alawite sect.