UN-Arab League envoy Lakhdar Brahimi's talks with Sergei Lavrov occurred a day after the main Syrian opposition group rebuffed diplomatic advances by Russia and firmly reiterated it would not negotiate with President Bashar Assad's government.
Brahimi is trying to build on an agreement reached in Geneva in June by world powers, including the United States and Russia, that called for the creation of a transitional government but left Assad's role unclear.
The mediator, who met Assad and others on a five-day trip to Syria, is to meet together with senior US and Russian diplomats in the coming weeks, after two such meetings this month that produced no signs of a breakthrough.
In Damascus on Thursday, Brahimi called for a transitional government to rule until elections in Syria and said only substantial change would meet demands of ordinary Syrians, but did not specify who could be part of the transitional body.
Russia has vocally supported Brahimi's efforts while refusing to join Western and Arab calls for Assad's exit, as it has throughout a conflict that has killed 44,000 people since protests in March 2011 elicited a fierce government crackdown.
Syrian Deputy Foreign Minister Faisal Makdad discussed Brahimi's proposals with Lavrov in Moscow on Thursday.
Lavrov on Friday urged the government and opposition to start a dialogue, and Russia said it had invited the leader of the National Coalition opposition group to meet Russian officials in Moscow or elsewhere for the first time.
The invitation and calls for dialogue were among signs that with the rebels advancing steadily over the second half of 2012, Russia may be reaching harder for a diplomatic solution than it did when it was more confident Assad could hold out.
But coalition leader Moaz Alkhatib said he had ruled out a trip to Moscow and suggested he would only meet Russian officials if Moscow condemned the Syrian government's actions and clearly called for Assad to step down.
An opposition spokesman said separately on Friday the coalition "will not negotiate with the Assad regime," also underscoring the uphill struggle Brahimi faces.
Russia, together with China, has angered the West and some Arab states by vetoing three UN Security Council resolutions meant to put pressure on Assad, who has given Moscow one of its firmest post-Soviet footholds in the Middle East.
President Vladimir Putin has said Russia is not trying to prop up Assad, contending that its vetoes and opposition to UN sanctions are driven by the principle of non-interference in sovereign states.
Russia has warned it will not allow a repeat in Syria of last year's events in Libya, where NATO intervention, authorized by the UN Security Council after Russia abstained from a vote, helped rebels topple Muammar Gadhafi.
MOSCOW (Reuters) -- The international mediator seeking to end the 21-month-old conflict in Syria met Russia's foreign minister in Moscow on Saturday after talks in Damascus but expectations of progress toward a negotiated solution were low.