A first round of discussions on Wednesday saw the two sides, having their first contact since 2003, restate well-known positions with little sign of compromise, diplomats said.
The island's Tamil-dominated north and east has largely been calm since 25 January when the two sides agreed to meet, but if the Geneva talks collapse, many fear the end of a 2002 truce and a return to a civil war which has killed more than 64,000 people.
Diplomats say the talks, at a chateau outside Geneva, would be a success if the two simply agreed to meet again, and perhaps outlined some confidence-building measures.
Both accuse each other of violating the fragile truce, with some 200 people killed in December and January.
But they differ on what needs to be done. The government wants to strengthen conditions of the ceasefire, but rebels say Colombo must crack down on paramilitary groups, particularly one led by renegade Tamil rebel leader Colonel Karuna.
Tamil Tigers routinely deny the
involvement of child soldiers
Anton Balasingham, the chief Tigers' negotiator, told the government delegation and Nordic mediators: "The armed violence of the Tamil paramilitaries is posing a grave threat to peace and stability in Tamil areas and endangering the ceasefire."
Nimal Siripala de Silva, the government delegation leader and health minister, countered that the ceasefire was not working and needed revamping because the Tigers were using it to re-arm.
The Tigers want a separate homeland for minority Tamils in north and east Sri Lanka, where they run a de facto state.
Mahinda Rajapakse, the president, has ruled out a separate Tamil homeland - a stance the rebels branded as childish. But, in what was seen as a conciliatory gesture, he has vowed to bring armed groups under control.
Erik Solheim, the Norwegian envoy who brokered the meeting, admitted suspicion ran deep. "Confidence can only increase, but it starts at a low level," he said.
The issue of child soldiers was to have been addressed on the first day of talks, on which all sides have agreed a news blackout, along with the paramilitary groups, analysts said.
But progress was likely to have been slow given that the Tigers routinely deny any child recruitment.