The sides cannot agree on the future role of President Bashar al-Assad.
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.
For a very long time we have had to depend on the aid that we had inside the besieged area. We are in 13 districts that are totally under siege.
We have reached a point where all the aid we have has now finished, and we are now eating anything that comes out of the ground, even grass. We pick it, then cook it with some water, using wood because we have no gas. Oil and petrol are also cut off from the besieged areas.
The shrubs and grass that we're eating cause illnesses. A few days ago an elderly man died within six hours from eating the grass and shrubs.
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.
Syrian presidential advisor Bouthaina Shaaban: "We want to continue talking"
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.
UN mediator Lakhdar Brahimi says both sides must "respect the confidentially of the discussions"
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.
Louay Safi, National Coalition: "The senior members of the regime delegation... are still outside the room"
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. http://www.bbc.co.uk/news/world-middle-east-25908347