Moscow has said it will hold talks with the US aimed at a total withdrawal of rebel forces from eastern Aleppo
Russia and China have vetoed a resolution at the UN Security Council calling for a truce in Aleppo.
The proposal - put forward by New Zealand, Egypt and Spain - called for a seven day truce in the Syrian city.
China and Venezuela also voted against the resolution.
The US deputy ambassador to the UN Michele Sison says Russia's veto is frustrating.
"We remain directly engaged with key countries, including Russia, to address the horrific situation on the ground," she said. "But we will not let Russia string along this Security Council while waiting for a compromise from the Russians that never seems to come".
Meanwhile, two Russian nurses have been killed by rebel shelling at a makeshift field hospital in Aleppo, Russian officials say.
Major General Igor Konashenkov accused the United States, Britain and France of tipping off the rebels about the hospital's location.
A third Russian, a paediatrician, remained in a critical condition after the attack in the government-held Furqan neighbourhood of western Aleppo.
An unspecified number of Syrian residents were also injured, Major General Konashenkov said.
It came as Russian foreign minister Sergei Lavrov said Moscow would hold talks with the US aimed at a total withdrawal of rebel forces from eastern Aleppo.
There was no immediate comment from Washington, which has backed some of the rebels.
Bashar al Assad's forces have been continuing their sweeping advance in the eastern part of the city. They have seized two-thirds of the former rebel bastion since mid-November.
Russia, a staunch ally of Syria, says it is not involved in the current offensive, which has seen the army pound the east with airstrikes, barrel bombs and artillery fire.
The rebels are now reduced to an area just kilometres across. Fierce clashes between Assad forces and rebels took place around the Old City on Monday.
Mr Lavrov said the talks with the US would be aimed at ensuring a complete rebel evacuation from the city and could begin as early as Tuesday in Geneva.
"During the Russian-American consultations the concrete route and timeframe for the withdrawal of all fighters from eastern Aleppo will be agreed upon," he said.
"As soon as these routes and timeframes are agreed on, a ceasefire can come into effect."
He added: "Those armed groups who refuse to leave eastern Aleppo will be considered to be terrorists.
"We will treat them as such, as terrorists, as extremists and will support a Syrian army operation against those criminal squads."
Rebel groups have swiftly rejected any talk of an evacuation.
Yasser al Youssef, of the Nureddine al Zinki faction, a leading rebel group in Aleppo, said any such proposal was "unacceptable".
"It is for the Russians to leave," he told AFP news agency.
Another rebel official, Zakaria Malahifji, said: "No person in his right mind, who has any sense of responsibility and patriotism, would leave his city."
But another opposition official, who declined to be identified, told Reuters news agency that they may have no alternative for the sake of civilians who have been under siege for five months and faced relentless government bombardments.
"The people are paying a high price, with no state or organisation intervening," the official said, adding that this was his personal assessment based on reports from the city.
If Washington and Moscow were to agree a deal for rebels to evacuate Aleppo, it would mark the first time the two powers, which back opposing sides in the civil war, have negotiated the withdrawal of opposition forces.