GAM was pushing for Jakarta to allow local Achenese, including former rebels, to form their own political parties.
Indonesian President Susilo Bambang Yudhoyono and other government leaders have said that local parties would not be allowed to stand in elections in Aceh as that would violate the law, but former GAM members would be allowed to stand as candidates for national parties.
The current round of talks aimed at ending three decades of violence in Aceh province were due to continue through Sunday and are mediated by former Finnish President Martti Ahtisaari.
"They will continue as long as possible, every hour is needed,'' Maria-Elena Cowell, spokeswoman for Ahtisaari's Crisis Management Initiative (CMI) said, adding the parties appeared willing to resolve their differences.
The fifth round of talks opened Tuesday with conciliatory statements by both sides.
"While they are still talking there is always hope,'' Damien Kingsbury, an Australian academic who advises GAM, told Deutsche Presse-Agentur dpa by telephone from Helsinki.
According to Kingsbury the two sides had agreed in principle on allowing the European Union and some member states of ASEAN to help monitor a possible agreement.
After the former round, Ahtisaari said there was need to monitor the decommissioning of arms and the withdrawal of national forces and police.
Talks resumed in January under Ahtisaari's mediation following a massive earthquake and tsunami on December 26 that left more than 167,000 people dead or missing in Aceh, on the northern tip of Sumatra. dpa lsm sc
- Deutsche Presse Agentur
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