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Bogdanov, the Kremlin's special envoy for Middle East Affairs, said the three would meet again in January after the holiday period.
Russia has also invited the head of the internationally-recognized opposition Syrian National Council, Moaz al-Khatib, to talks, he said, in comments that appeared underline Moscow's commitment to helping Brahimi seek a way out of the crisis.
Russia has been critical of the Western backing for the Syrian National Council trying to oust Assad.
Brahimi, who has called for a transitional government to rule until elections, is trying to broker a peaceful transfer of power in Syria, where more than 44,000 people have been killed in a revolt against four decades of Assad family rule.
What role Assad and members of his government might play in a transitional body – a plan outlined in Geneva six months ago – has divided world powers.
Past peace efforts have floundered as what began as peaceful protests in March 2011 turned into civil war. The conflict has become an increasingly sectarian struggle between mostly Sunni Muslim rebels and Assad's security forces, drawn primarily from his Shi'ite-rooted Alawite minority.
World powers believe Russia, which has given Assad military and diplomatic aid during the uprising, has the ear of Syria's government and must be a central player in any peace talks.
Moscow has tried to distance itself from Assad in recent months and has denied it is not propping him up. But it maintains Assad's exit cannot be a precondition for talks and has repeatedly said Western powers should not impose solutions on Syria.
Lavrov warned yesterday that time was running out to find a peaceful solution to the conflict and halt a descent into "bloody chaos."