Pulled together by the UN, Russia and the United States, delegations from President Bashar al-Assad's regime and the opposition had been due to sit down at 11:00 am (1530 IST) at UN headquarters in Geneva.
UN mediator Lakhdar Brahimi spent yesterday trying to convince them to be in the same room for the start of the talks -- the biggest diplomatic effort yet to stem the bloodshed in Syria's devastating civil war.
"Both meetings will be bilateral," she said.
"This process is shaping up, so there have been changes to previous declarations," Vellucci said. "We are going step by step."
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Sources within the delegations told AFP the opposition had refused to sit in the same room unless the regime accepted the need for a transitional government without Assad.
Syrian Deputy Foreign Minister Faisal Moqdad told reporters the opposition was obstructing the talks.
"The problem is that these people do not want to make peace, they are coming here with pre-conditions," he told reporters.
Nazir al-Hakim, a member of the opposition delegation, told AFP it was only willing to negotiate on the basis of the agreement reached at the "Geneva I" peace conference in 2012, which called for the creation of a transitional government.
"We agree to negotiate on the application of Geneva I. The regime does not accept that," he said.
"We will be in the same room when there is a clear agenda for negotiations. We need guarantees that Geneva I will be discussed," Hakim said.