The sources said the talks had broken up with no progress after the delegation from President Bashar al-Assad's regime set out a statement of principles aimed at preserving state institutions and stopping the threat from "terrorist" groups.
The opposition rejected the statement, saying talks needed to focus on a political transition, and UN mediator Lakhdar Brahimi ended the session, the sources said.
"The discussions were not constructive today because of the regime's strategy to deflect... (and) change the subject by talking of terrorism," Rima Fleihan, a member of the opposition National Coalition's delegation, told reporters.
A source close to the regime delegation told AFP the opposition had rejected discussion of anything other than the creation of a transitional government.
"The government delegation presented a statement on essential principles to save Syria, the State and its people from extremist terrorism," the source said.
"As soon as it finished the Coalition rejected this statement and demanded that we talk only of a transitional body. Mr Brahimi then adjourned the session," the source said.
The day marked the third day of UN-sponsored talks between the two sides in Geneva and the first expected to deal with political issues.
The opposition says Assad must leave power and a transitional government be formed based on an agreement reached during a first peace conference in Geneva in 2012.
The regime says Assad's role is not up for debate at this conference -- dubbed Geneva II -- and denies that the initial Geneva deal requires him to go.