Russia said Monday it would hold talks with Washington on a total rebel withdrawal from Syria's Aleppo, where the army has made sweeping advances, but opposition factions rejected any evacuation.

President Bashar al-Assad's forces have seized two-thirds of the former rebel bastion in east Aleppo since they began an operation to recapture all of the battered second city in mid-November.

The assault has raised an international outcry, but Russia and China Monday vetoed a UN Security Council resolution calling for a seven-day ceasefire in the city.

Tens of thousands of east Aleppo residents have fled to other parts of the city from the fighting, which has raised widespread international concern.

The rapid regime gains have left opposition fighters reeling, and earlier Monday Russian Foreign Minister Sergei Lavrov said talks would be held on a rebel evacuation.

"During the Russian-American consultations the concrete route and timeframe for the withdrawal of all fighters from eastern Aleppo will be agreed upon," Lavrov said, adding the discussions in Geneva would probably start on Tuesday or Wednesday.

"As soon as these routes and timeframes are agreed on, a ceasefire can come into effect," Lavrov said.

But rebel groups swiftly rejected any talk of an evacuation.

Yasser al-Youssef of the Nureddine al-Zinki faction, a leading rebel group in Aleppo, described any such proposal as "unacceptable".

"It is for the Russians to leave," he told AFP.

Moscow is a close ally of Assad's government, and launched a military intervention in support of Damascus last year.

Government troops have also been bolstered by Iranian forces, fighters from Lebanon's Shiite Hezbollah movement and Shiite fighters from other countries.

- 'Revolutionaries won't leave' -

"The revolutionaries will not leave Aleppo and will fight the Russian and Iranian occupation until the last drop of blood," said Abu Abdel Rahman al-Hamawi of the Army of Islam, another smaller rebel group active in Aleppo.

Rebels have been forced to evacuate several of their strongholds in Syria during the conflict, including a string of areas near Damascus in recent months.

In many instances, they have reached deals with the government after months of army siege and fierce fighting, agreeing to lay down their arms in return for safe passage to rebel territory elsewhere.

Among the most well-known evacuations was the 2014 exit of rebels from the Old City of Homs after a two-year government siege.

But if Washington and Moscow were to agree a deal for a rebel evacuation from Aleppo, it would mark the first time that the two powers, which back opposing sides in the war, have negotiated the withdrawal of opposition forces.

Estimates for the number of rebels in east Aleppo vary, with the Britain-based Syrian Observatory for Human Rights monitor putting the figure at 15,000 before the current assault began.

The UN's Syria envoy Staffan de Mistura in October put the number at 8,000 rebels, saying around 900 of them belonged to the Fateh al-Sham Front, Al-Qaeda's former Syrian affiliate previously known as Al-Nusra Front.

The loss of Aleppo would be the biggest defeat yet for opposition forces in Syria's five-year civil war.

- Army pounds east Aleppo -

Russia is a staunch ally of Syria's government, and began a military intervention in support of Damascus in September 2015.

It says it is not involved in the current offensive in Aleppo, which has seen the army advance quickly as it pounds the east with air strikes, barrel bombs and artillery fire.

But Moscow has sent field hospitals to the city, and said Monday one of the facilities was hit by rebel fire, killing two Russian army medics and wounding another.

On the ground in the east, Syrian troops battled rebels in the Shaar district, which the army has almost completely encircled after advancing overnight.

The army on Monday pounded remaining rebel territory with incessant strikes and artillery fire that sent up plumes of smoke visible from across the city.

The Observatory says at least 324 people have been killed in east Aleppo during the offensive, including 44 children.

Rebel fire into the government-held west of the city has killed 73 people, including 29 children, in the same period, the monitor says.

On Monday, state news agency SANA said eight people had been killed in rebel fire on west Aleppo, and an AFP correspondent in the west reported heavy incoming rocket fire that shook buildings.