Delegations from President Bashar al-Assad's regime and the opposition National Coalition sat down from around 11:00 am (1000 GMT), the UN said.
The two sides have been unable to even begin discussing political questions, let alone the core issue of creating a transitional governing body.
There has been disappointment over the failure to agree any humanitarian measures, especially for besieged residents in the central city of Homs, where UN trucks are waiting for access to deliver food and medical aid.
The opposition said it had presented its "vision" of the way forward but that the regime had refused to discuss it.
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"Nobody is walking out, nobody is running away," Brahimi told reporters yesterday. "We have not achieved any breakthrough, but we are still at it, and this is good enough as far as I'm concerned."
"Brahimi yesterday was very clear: the regime delegation must present its agenda and its vision of Geneva I," the source said.
The two sides have been brought together in the biggest diplomatic push yet to end a civil war that has left more than 130,000 dead and forced millions from their homes.
Expectations are low for a breakthrough, especially after the talks hit an impasse on Monday when the two sides failed to agree on even the basic principles of political talks.
In the only tangible promise to emerge from the meetings so far, Brahimi said Sunday the regime had agreed to allow women and children safe passage from besieged rebel-held areas of Homs.
But there has been no movement since, on either an evacuation or Brahimi's hope that aid convoys will be allowed in the areas.