On Tuesday, opposition leaders said they were ready to meet face-to-face.
But chief government negotiator Bashar al-Jaafari rejected the idea, calling his opposition counterpart a terrorist.
Meanwhile, Syria's main Kurdish party - which has not been invited to Geneva - plans to declare a federal system of administration in the country's north.
Officials from the Democratic Union Party (PYD), whose YPG militia controls a 400km (250-mile) stretch of contiguous territory along the Turkish border, said the system would include representation for all ethnic groups living there.
Mr Jaafari refused to comment on the plan but warned: "Betting on creating any kind of divisions among the Syrians will be a total failure."
He also explained after his second meeting with UN special envoy Staffan de Mistura that he would refuse to take part in direct talks with the opposition's chief negotiator, Mohammed Alloush, a member of the Jaysh al-Islam rebel group.
Mr Jaafari accused Mr Alloush of belonging to a terrorist organization that "bombed embassies" and "killed engineering students", and demanded that he "apologizes for the statement he made previously and withdraws it", without elaborating.
The so-called "proximity" talks currently involve Mr de Mistura shuttling between the two sides, communicating their different views on how to end the five-year conflict, in which more than 250,000 people have been killed.
Mr Jaafari's refusal to meet the opposition face-to-face shows that despite initial progress these talks will be difficult, reports the BBC's Imogen Foulkes in Geneva.
The Syrian government is clearly smarting over Russia's plan to withdraw most of its forces from Syria, our correspondent says.
Although Mr Jaafari insisted this was a decision taken jointly by Moscow and Damascus, she adds, all the signs are that President Bashar al-Assad was taken by surprise.