Russia makes Aleppo ceasefire ultimatum to Syrian rebels
But moderate rebel groups will have to leave areas where the Islamic State group and al-Nusra Front – Syria's al-Qaeda affiliate – operate.
This would hint that regime and Russian bombing of Aleppo would continue under the pretence of targeting "terrorist groups".
He also said that rebels would have to cut ties with Nusra, who have supported the rebels on some fronts in Aleppo, including against IS.
Many believe this amounts to an ultimatum to Syrian rebels to leave Aleppo.
"That is one of the main topics we are discussing with our American colleagues," Lavrov said. He also urged Washington to put pressure on moderate rebels.
"Those who consider themselves moderate (opposition) should unconditionally break with any terrorist groups, first and foremost with al-Nusra Front," he added in televised remarks.
Aleppo has been heavily bombed by regime and Russian war planes, leading to over 250 dead in one week.
Lavrov, a firm supporter of Bashar al-Assad's regime, said a cessation of hostilities in Aleppo could be announced shortly.
"I am hoping that in the near future, maybe even in the next few hours such a decision will be announced," Lavrov told reporters after talks with UN envoy Staffan de Mistura.
Russia and the US will report on violations of the ceasefires in Syria through a joint monitoring centre.
Ceasefires had been announced in Eastern Ghouta, near Damascus city and Latakia, but Aleppo – which has suffered from ferocious regime assault – was left out of the truce.
Earlier, the Syrian regime said it would extend the ceasefire in eastern Ghouta by another 24 hours, despite reports of a build-up of Hizballah and pro-Damascus troops in the vicitinty.
Meanwhile, an infra-rebel conflict has broken out in the Damascus suburbs which is part of the ceasefire between members of Jaish al-Islam and al-Nusra Front affiliated militias.
Syria's larger two-month ceasefire has all but ended, while talks between the UN, US and Russia have taken place in a bid to find an end to the war.
Germany has also offered to hold talks to help bolster prospects of an eventual peace deal.
"[It will be for] how the conditions for a continuation of the peace talks in Geneva can be met, as well as how a reduction of violence and an improvement in the humanitarian situation in Syria can be achieved," the German foreign ministry said in a statement.
The Syrian opposition are sceptical about US-Russian plans, particularly as Moscow has taken a leading role in bombing of rebel areas in Aleppo.
Washington has also offered little more than mild condemnation of the most recent regime assault on Syria's second city.
Bombing and shelling has continued over the past two days, but markedly down since last week's air raids which killed dozens each day and destroyed two hospitals.