UN mediator Lakhdar Brahimi said there “was apparently the will” to continue talks but “we never expected any miracles”.
He said there was no decision yet on allowing an aid convoy into besieged areas of the city of Homs.
“We are happy and encouraged that this conference has taken place – it is one little step forward but whatever gain we have made is reversible.
“We will continue trying to make this work and we hope that both parties will co-operate,” Mr Brahimi told a news conference in Geneva.
The peace talks resumed in Geneva on Monday morning. The Syrian government team presented a “declaration of principles” that did not mention transfer of power; it was rejected by the opposition.
The declaration reportedly demanded that Syrians choose a political system without “imposed formulas” from outside – an apparent reference to attempts to remove Mr Assad – while also insisting on discussing “terrorism” rather than transfer of power.
The opposition insists that the regime commits in writing to the Geneva I communique, which calls for a transition process.
Rima Fleihan, a member of the opposition National Coalition’s delegation, said: “The discussions were not constructive today because of the regime’s strategy to deflect [and] change the subject by talking of terrorism.”
Mr Brahimi adjourned the session, and held separate talks with both parties later on Monday.
The negotiations are expected to resume on Tuesday, when both sides will discuss the Geneva I communique.
One of the elements is the composition of a governing body with full executive powers, but Mr Brahimi said this was “the most complicated of matters” and would almost certainly not be discussed first.
He also called on both parties to refrain from speaking in too much detail to the media, saying the “confidentiality of the discussions” should be respected.
‘Regime must act’
The UN plan to send humanitarian aid to Homs, where hundreds of people have been trapped in the Old City since June 2012, was also discussed.
The government said on Sunday that women and children were free to leave the city, and there were hopes a humanitarian convoy would set off on Monday.
Mr Brahimi said the government was “willing to make it happen” but cited security problems for part of the delay.
An opposition delegate in Geneva, Monzer Akbik, said 12 trucks from the Red Crescent were waiting to go in.
“The city of Homs, the Old City of Homs, is still under starvation siege,” he said.
On Monday, the US said Syria’s evacuation offer was not sufficient, insisting that all civilians should be permitted to leave and aid convoys allowed in.
State department spokesman Edgar Vasquez said: “The situation is desperate and the people are starving.
“There should be no reason for delay. The regime must act now.”
One journalist inside Homs told the BBC that aid in the besieged areas had run out and people were eating grass and shrubs. He said those who fell sick had no access to medicine and no way of leaving the area.
“We are under deadly siege. If we don’t die from bombardment or snipers, we die of hunger or the cold,” he said.
Syria’s civil conflict has claimed well over 100,000 lives since it began in 2011.
The violence has also driven 9.5 million people from their homes, creating a major humanitarian crisis within Syria and for its neighbours.