Meeting in the Moroccan city of Marrakech as rebels battled Mr Assad's troops on the outskirts of Damascus, the Friends of Syria group called on the President to step aside and warned him against using chemical weapons.
At the same meeting, the leader of Syria's opposition coalition called on the Alawite minority to launch a campaign of civil dis-obedience against Mr Assad, an Alawite who faces a mainly Sunni Muslim uprising against his rule.
Hours earlier, President Barack Obama announced Washington would now recognise the coalition of opposition groups as Syria's legitimate representative, joining France, Britain, Turkey and Gulf states.
"Participants acknowledge the National Coalition as the legitimate representative of the Syrian people and the umbrella organisation under which the Syrian opposition are gathering," said a draft declaration of the Marrakech meeting. The gathering brought together many western and Arab nations opposed to Mr Assad, whose family has ruled Syria for 42 years but excludes Russia, China and Iran, which have backed the President or blocked efforts to tighten pressure on him.
"Bashar al Assad has lost legitimacy and should stand aside to allow a sustainable political transition," said the text.
Referring to Western intelligence reports suggesting Syria might use chemical and biological weapons, it said "this would draw a serious response from the international community".
Opposition coalition member Abdelbasset Sida said diplomatic recognition would not be enough. "We need military support. A transitional phase has started, and we need the means to defend the liberated parts of Syria."