Talks to 'distance' Syrian rebels from former al-Qaeda group
Russia has repeatedly demanded that rebels break off ties from the former al-Qaeda affiliate, which rebranded in July after cutting ties with Ayman al-Zawahiri.
They have made the departure of the militants in rebel areas - said to number in the hundreds - a condition for a more lasting ceasefire in Syria, following a year of bombing by Moscow, killing thousands of civilians.
"Those countries did express their intention to work hard with those moderate opposition groups in order for them to be separated from al-Nusra," Russian Ambassador Vitaly Churkin told reporters, referring to Fatah al-Sham's former name.
The United Nations Security Council met behind closed doors to discuss the latest talks held in Luasanne, Switzerland, over the weekend.
Churkin said Fatah al-Sham fighters must be forced to leave Aleppo "or they will have to be defeated" and said their departure would pave the way to a ceasefire.
The presence of small numbers of fighters in the city have been used as a pretext by Russia and the Syrian regime to bombard east Aleppo.
If the Nusra fighters leave, "the understanding of Lausanne is that then the moderate opposition and the Syrian government will enter into cessation of hostilities negotiations which will make it possible to prevent further bloodshed and prevent loss of life", he said.
The Russian envoy cited figures from UN envoy to Syria Staffan de Mistura that some 900 fighters in Aleppo were from Fatah al-Sham, compared to some 10,000-12,000 opposition rebels. This has been disputed by Syrian opposition, who say there are as few as 150 fighters.
De Mistura earlier this month offered to personally escort the extremists out of Aleppo to avoid the destruction of the city by air strikes.
The US designated the-then al-Nusra Front a terrorist organisation in November 2012, and did not reassess this status following its name change.
Its existence at the al-Qaeda end of the spectrum of groups operating in Syria means that Fatah al-Sham has been a target for air strikes by both Russian and US-backed military action.
Russia on Monday announced plans for an eight-hour pause in fighting in Aleppo, which will take place on Thursday and says this would allow for free passage of civilians, the evacuation of the wounded and the withdrawal of fighters.
Previous attempts at creating evacuation corridors in Aleppo have failed, with civilians afraid of heading to regime areas, and other ceasefires broken by Moscow and Damascus.