United Nations Secretary-General Ban Ki-moon has pushed for the 193-member General Assembly to hold a rare emergency special session on Syria.
A deadlocked Security Council has so far failed to take action to end the nearly six-year war.
Under a 1950 resolution, an emergency special session can be called for the General Assembly to consider a matter "with a view to making appropriate recommendations to members for collective measures" if the Security Council fails to act.
"I call on all of you to cooperate and fulfil your collective responsibility to protect," Ban said.
"I regret that the Security Council has failed to discharge its responsibilities to uphold peace and security for Syria."
Russia, a Syrian ally that has been providing military backing to the Syrian government for the past year, has vetoed five Security Council resolutions on Syria since 2011.
China joined Moscow in vetoing the first four resolutions.
Ban and UN Syria envoy Staffan de Mistura informally briefed the General Assembly on Thursday at the request of Canada and more than a third of UN states.
In its request letter, Canada said one aim of the meeting was to see if there was enough support for an emergency special session.
Such a session can be called by an assembly majority or nine members of the 15-member Security Council.
Only 10 such sessions have been convened, and the last time the General Assembly met in such a session was in 2009 on Israeli actions in occupied Palestinian territories.
An emergency special session of the General Assembly could adopt a resolution on Syria recommending action.