Air strikes pummelled the shrinking rebel enclave in Aleppo on Saturday as US Secretary of State John Kerry said the Syrian regime's "indiscriminate bombing" amounted to crimes against humanity.

Western powers meeting in Paris called for the resumption of peace talks and for civilians to be allowed to leave Aleppo, where tens of thousands have already fled a fierce regime offensive.

The diplomatic flurry came as a US-backed alliance announced it would launch the second phase of its battle for the Islamic State group's de facto Syrian capital Raqa further east.

The three-week-old assault by Syria's Russian-backed regime aimed at retaking all of Aleppo has triggered mounting international outrage.

"The indiscriminate bombing by the regime violates rules of law, or in many cases, crimes against humanity, and war crimes," Kerry said after the talks in Paris, urging Russia to do its "utmost to bring it to a close".

US and Russian officials meanwhile were due to gather in Geneva for what Kerry described as a bid to stop the city from "being absolutely, completely, destroyed".

Aleppo has witnessed some of the most brutal violence of the country's nearly six-year war.

In less than a month, forces loyal to President Bashar al-Assad have overrun around 85 percent of east Aleppo, a rebel stronghold since 2012.

The UN's Syria envoy Staffan de Mistura said the world is watching "the last steps" in the Aleppo battle and evacuating civilians must be a priority.

Air strikes and regime rocket fire battered the last remaining rebel districts on Saturday, the Syrian Observatory for Human Rights said.

An AFP correspondent in west Aleppo could hear the hum of airplanes circling above, coupled with bombardment and machine-gun fire on the city's east.

The strikes were so intense that windows in the west rattled and plumes of smoke could be seen rising from several points across the city's skyline.

- 'People under the rubble' -

"The bombing is unreal," said Ibrahim Abu al-Leith, spokesman for the White Helmets rescue force inside Aleppo.

Abu al-Leith spoke to AFP from one of the last rebel-controlled zones in Aleppo's southeast, saying he had been forced to move homes because of the intensity of the raids.

"The streets are full of people under the rubble. They are dying because we can't get them out," he added.

According to the Observatory, nine civilians were killed on Saturday in a barrage of rebel rocket fire on government-controlled neighbourhoods.

The fresh attacks brought to 129 people, including 39 children, the number of people killed by rebel fire on regime-held west Aleppo since November 15.

Another 413 civilians, among them 45 children, have been killed in east Aleppo in the same period.

With the fighting intensifying after a brief respite, the UN General Assembly demanded an immediate ceasefire and urgent aid deliveries, in a resolution adopted by a strong majority.

But both Moscow and Damascus have rejected talk of a ceasefire without a rebel withdrawal from the city -- a demand that opposition groups have refused.

After meeting with opposition representatives on Saturday, French Foreign Minister Jean-Marc Ayrault said the opposition was willing to resume peace talks "without pre-conditions".

Retired American general David Petraeus, a possible contender to replace Kerry when Donald Trump becomes US president next month, expressed doubt about prospects for a political solution in Syria.

"It is not clear that Humpty Dumpty can be put back together again," he said at a security forum in Bahrain. "I don't think it's too late for that but I do think that it is very late in the day indeed."

- Civilian exodus -

The Observatory said another 2,000 civilians poured out of Aleppo's remaining rebel-held districts on Saturday.

State news agency SANA also reported the displacement, but gave a number of 3,000 people and said they had been taken to the temporary shelter in Jibrin, about 10 kilometres (six miles) east of Aleppo.

The UN said Friday it had received reports of rebels blocking some from leaving and of reprisals against residents who asked armed groups to leave.

It has also expressed concern about reports that hundreds of men had gone missing after fleeing to government-held territory.

The fall of east Aleppo would be the biggest blow for the rebels since the war began in 2011.

It began as a widespread protest movement against Assad's regime but has since evolved into an all-out war that has seen jihadists like the Islamic State group rise to prominence.

On Saturday, the US-backed Syrian Democratic Forces announced "phase two" of the campaign for the jihadist bastion of Raqa.

Washington announced it was sending an additional 200 troops to support the offensive.