Syrian envoy calls for political change
"What is preferred is that we don't present such a plan until we feel that all sides have agreed to it. That way, implementing it is easy. If that doesn't happen, the other solution could be to go to the (United Nations) Security Council to issue a binding resolution for everyone," he said.
A Russian foreign ministry spokesman also denied any joint initiative between Moscow and Washington.
World powers remain divided over what has become an increasingly sectarian struggle, with Sunni Muslim states such as Turkey and the Gulf Arab countries supporting the rebels while Shia Iran and Hezbullah have backed Assad, whose Alawite community has its roots in Shia Islam.
Syria's struggle "has taken a vicious form of sectarian confrontation," Mr Brahimi said. "Syrian officials foremost, as well as the international community, must not let Syria slide down this very dangerous path which threatens the future of Syria."
Deep differences between Western powers opposed to Assad - led by the United States - and Russia and China which have supported his government, have left the UN Security Council paralysed and largely sidelined throughout the conflict.
The political stalemate has helped transform a once-peaceful uprising into a civil war in which rebels have grown in military strength and taken control of swathes of territory in the north, leaving Assad increasingly reliant on air power to curb them.
Activists in the central province of Hama, where rebels launched an offensive last week to extend their control southwards towards the capital, reported on Thursday that rebels shot down a MiG jet near the town of Morek.
The Syrian Observatory for Human Rights, which monitors violence across Syria, said air force jets launched three raids on rebel forces around Wadi Deif. The British-based group also reported fierce clashes in the area.
The violence has been accompanied by an escalation in apparently sectarian attacks between the Sunni Muslim majority and minorities such as Assad's Alawite sect, which has largely supported the president.
Activists in Hama uploaded a video of what appeared to be Assad soldiers and shabbiha militia members stabbing the body of a dead man and setting it on fire. The man looked as if he had been beaten to death.
"This is a terrorist, a brother of a whore, one of those trying to destroy the country," one of the men shouted. Two men in camouflage uniforms and army helmets stood by watching.
Samer al-Hamawi, an activist from Hama, said rebels in his area found the video on the phone of a soldier they captured this week. The video emerged a day after Islamist rebel units released footage showing the bodies of dozens of Assad's fighters along a highway near an Alawite town in Hama.