Indonesia is scheduled to sign the agreement with GAM on Aug. 15 to end decades of bloody conflict that has claimed the lives of more than 12,000 people, mostly civilians.
"Amnesty will be given by the latest 15 days after the signing," minister Sofyan Djalil told reporters.
This could mean thousands of convicted rebels would be released from jail in Aceh and other parts of Indonesia once the amnesty is announced.
However, Indonesian officials have said they would not grant amnesty to GAM rebels jailed for pure criminal offences such as robbery and killings.
Other details of the process remain sketchy but normally political prisoners must declare their allegiance to Indonesia before being released.
GAM has been fighting for Acehnese independence since 1976 but in the peace talks that began in Helsinki in January this year the GAM side dropped that as a condition for an agreement.
Jakarta has promised to grant amnesty in a bid to meet demands by GAM members to restore their political rights in order to allow them to compete in local elections in Aceh on Sumatra island's northern tip.
The peace talks and deal got some of their impetus from the Dec. 26 tsunami that left nearly 170,000 people dead or missing in Aceh, hardest hit by the disaster.
Foreign donors responsible for the bulk of a $5 billion recovery programme are eager to see a peace deal that would ensure security and smooth the rebuilding process.
An observer team from the European Union and Indonesia's Southeast Asia neighbours will monitor implementation of the peace deal.
Some of the EU observers were in Jakarta on Monday to hold closed-door meetings with Indonesian authorities.
- Reuters - Thomson Reuters Foundation
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