Syria's ambassador to the United Nations, Bashar al- Jaafari, was heading the government delegation for the four days of meetings with members of the domestic "tolerated" opposition, the National Coordination Committee for Democratic Change (NCCDC).
The talks were to begin at 1430 IST, a source close to the negotiations said.
But the main Western-backed exiled Syrian opposition National Coalition stayed away, and another leading domestic opposition activist remains under a travel ban from Damascus.
The closed-door discussions are expected to focus on humanitarian issues and serve as a way for Russia, a main backer of the Syrian regime, to build its profile as a potential mediator in the conflict.
They follow a similar round of meetings between the government and officially tolerated opposition in Moscow in late January that failed to make any concrete progress towards resolving the deep-rooted conflict.
The sit down is the first since some of the key international players in the crisis thrashed out an outline deal over Iran's nuclear programme and US Secretary of State John Kerry refused to rule out speaking to Syrian President Bashar al-Assad.
But despite the seemingly positive noises over the conflict there seemed little prospect of any breakthrough at the Moscow talks.
Ahead of the meeting a source close to Syrian government delegation said that the delegations "will only discuss 'soft' subjects on which agreement might be found."
"You cannot say that these consultations will have any major results," Russian Middle East expert Boris Dolgov said.
"It is just one step, albeit important, on the path towards stopping the crisis in Syria."
Dolgov said that by hosting the talks Moscow -- a firm backer of Assad's regime -- was looking to boost its standing as a potential mediator while also seeking to curb the threat that radical groups such as Islamic State pose to its national security.
The opposition National Coalition, however, accusing Russia of seeking to use the talks to bolster Assad, has declined to attend, and finds itself increasingly sidelined by powerful regional actors such as Saudi Arabia and Egypt.

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