The main Syrian opposition on Friday called on the UN Security Council to put greater "international pressure" on President Bashar al-Assad to come to negotiations.
The coalition also said Russia should stop providing weapons to Assad's "criminal regime."
But the first meeting between the Syrian National Coalition and the 15-member Security Council gave few signs of progress in efforts to end the conflict, which the United Nations says has left more than 100,000 dead.
"We need far more international pressure to force the Assad regime to accept a political transition," new coalition president Ahmad Jarba said he told the council.
Jarba made no direct appeal for arms, but said "as long as the Assad regime is waging war against the Syrian people, the opposition must have the right to self-defense."
The coalition has been on a tour seeking to make clear its political objectives and press for Western arms.
Jarba and other top coalition leaders met with French President Francois Hollande in Paris on Wednesday and with US Secretary of State John Kerry in New York on Thursday.
At each stop they asked for weapons to be quickly supplied to halt the killing of civilians.
The Security Council held an informal meeting with the coalition, because Russia, Assad's main international backer, said an official meeting would confer recognition on the opposition group, according to diplomats.
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"We asked them (Russia) to stop providing the political and military support for this criminal regime to continue its crimes against the Syrian people," Najib Ghadbian, the coalition's representative in the United States, said after the meeting.
Britain's UN ambassador Mark Lyall Grant, whose country organized the meeting, said the opposition had put across a "positive" message opposing extremism and backing democracy in Syria.
There was little sign however of a breakthrough in efforts to organize a follow-up to the Syria peace conference held in Geneva last year.
Russia and the United States vowed in May to work with UN envoy Lakhdar Brahimi to press for a follow-up conference to find a way to implement a transition plan agreed in Geneva.
The coalition opposes any role for Assad in a transitional government and insists that it must have full control of the army and security forces.
"Clearly there are still some obstacles to be overcome" for a new peace conference, Russia's UN envoy Vitaly Churkin said.
He added that opposition calls for Assad to step aside were "a precondition which creates problems" for organizing a new conference.
"I think members of the Security Council will have been encouraged by the commitment shown by the opposition," Lyall Grant told reporters when asked about the chances of a new conference.
"It remains to be seen whether the regime is equally committed."