Talks in Finland between a top-level Indonesian delegation and separatist leaders from Aceh province are reported to have got off to a good start.
Peace hopes have risen in the wake of the tsunami disaster
The first day was "very constructive", said mediators.
The Indonesian side, including three ministers, met leaders from the Free Aceh Movement (Gam) outside Helsinki.
The talks, brokered by Finland's former President Martti Ahtisaari, mark the first contact between the two sides for nearly two years.
The Asian tsunami, which killed more than 220,000 people in Aceh, seems to have given a new impetus to both sides.
Few observers believe there are any easy ways to bridge differences deepened by years of bitter conflict, reports Tim Johnston from Jakarta, but they now see the best chance for peace in many years.
Six weeks ago, there was deadlock in Aceh after almost two years of intense military operations failed to rid the province of the rebel insurgency.
But the massive earthquake and tsunami on 26 December have proved to be a springboard for talks to end a conflict that has claimed more than 13,000 lives, our correspondent says.
'No military answer'
Friday's meeting was the first time the government and rebels had held formal discussions since May 2003, and was being hosted by Mr Ahtisaari's Crisis Management Initiative (CMI).
ACEH: KEY FACTS
Gas-rich province on the north-western tip of Sumatra
Higher percentage of Muslims than other parts of Indonesia
Gam rebels have fought decades-long separatist campaign
Internationally-brokered peace deal brokered in Dec 2002 but collapsed in May 2003
Year-long military crackdown weakened Gam, but failed to capture senior members
"The meeting was very constructive and was carried out in a positive spirit," said Paullina Arola, executive director of the CMI.
The Indonesian government team is being led by Justice Minister Hamid Awaluddin.
The delegation from Gam, whose exiled leaders are based in neighbouring Sweden, is being led by self-styled Prime Minister Malik Mahmud and Foreign Minister Zaini Abdullah.
A Gam spokesman said earlier that the rebel movement wanted an informal ceasefire, which was agreed in the wake of the tsunami, to be formalised.
"Once we have done that, we will move on to other things," Nur Djuli told the BBC News website.
"It's not possible to settle a 30-year conflict in a few days, but it's quite clear militarily that both sides are going nowhere."
Indonesian President Susilo Bambang Yudhoyono has said he is willing to offer the rebels wide-ranging autonomy and other concessions in return for an end to their campaign.
"If we agree to terminate the conflict based on the special autonomy status, I will give some concessions to them," he said.
Jakarta has repeatedly rejected any demand for outright independence.
"We will consider options such as amnesty or assistance for Gam members who surrender, but one thing we cannot grant is independence," security ministry spokesman Demak Lubis told the French news agency AFP.
Another key Gam demand has been the full withdrawal of Indonesian forces from Aceh.
But Mr Yudhoyono said that while troops numbers would decrease if a ceasefire was announced, some soldiers would still remain in the province.
The talks in Finland, which will be held behind closed doors, are expected to continue until Sunday.