The two sides met separately the mediator, former Finnish president Martti Ahtisaari, and each other later on Tuesday.
"The atmosphere indicated that they are here with constructive minds and seriousness," said Maria-Elena Cowell, a spokeswoman for the Crisis Management Initiative, which has facilitated the talks.
Cowell said further talks are planned after the current six-day round finishes at the Konigstedt mansion in Vantaa, outside Helsinki.
Rebel leaders said before the talks they would demand Indonesian troops cease all anti-insurgency operations in Aceh before discussing a solution for self-government.
The rebel Free Aceh Movement, known locally as GAM, also demanded the release of four of their negotiators who were arrested by Indonesian authorities two years ago - despite a government guarantee of safe-conduct.
After a tsunami on 26 December devastated Aceh, the rebels proclaimed a unilateral truce saying they wanted to help rescue efforts.
But the Indonesian military said it would continue combat operations until a formal ceasefire was signed, and the army commander has claimed his troops killed nearly 200 rebels in the first two months after the disaster.
"Today's talks were conducted in a good spirit," Cowell said on Tuesday. "On the agenda were the Free Aceh Movement's demands of a ceasefire, and the amnesty of political prisoners."
She said there was no reply on those issues from the Indonesian government delegates, and the same issues would be on the table when talks continued on Wednesday.
Cowell said the meetings would also focus on bringing self-governance to Aceh, and the integration of GAM into Indonesian society as a political party.
In January, the two sides met face-to-face for the first time since the peace process collapsed in 2003, when the Indonesian military launched a major offensive against separatists in the oil-rich region that has killed about 3000 people.
A second round of talks was held late on February. Indonesia's vice-president has predicted an agreement could be reached by July on the basis of the so-called special autonomy law which the government in Jakarta adopted three years ago, but never implemented.
Human rights groups have accused government troops of executions, torture and rape of civilians in Aceh. They say most of those killed since the ceasefire collapsed have been unarmed villagers caught up in army operations.
The war in Aceh, one of the world's longest-running conflicts, has its roots in the occupation of the independent Aceh sultanate by Dutch colonialists in 1870.