House Speaker Agung Laksono opposed GAM's demand to form political parties as it violated Law No. 31/2002 on the establishment of political parties.
"The establishment of local parties will only create new problems. This is against the law on political parties," he said.
House members Effendi Choirie and Happy Bone Zulkarnain of Commission I concurred with Agung's opinion.
Meanwhile, Aceh-born legislator Ahmad Farha Hamid welcomed the accord as a way to end the conflict in the province.
"There is no problem with the establishment of regional political parties. We only need to review the law on special autonomy," he said.
Meanwhile, Vice-President Yusuf Kalla said the government would seek the legislature's approval for its proposal to allow GAM to form local political parties.
In another development, Indonesian Military Chief Endriartono Sutarto said that the government would send military troops to Aceh, if GAM broke its commitment to hand in their weapons as part of the peace accord agreed in Helsinki on Sunday.
"We will see their commitment if the reality in the field is different, we will send back military troops to Aceh. It is that simple," he said.
He said that if GAM had good intentions to uphold the Helsinki accord, they would hand over their weapons although there were still million of troops in Aceh.
The government has said it will withdraw its troops from the province once the rebels hand in their weapons.
The Indonesian government and GAM have reached a ground- breaking agreement to end 30 years of fighting in Aceh province and a memorandum of understanding will be formally signed next month.
The agreement is to bring a "peaceful, comprehensive and sustainable solution" to end conflict in the province.
Both sides also agreed to establish an Aceh monitoring mission to check on progress, which they hope will be run by the European Union and a number of Asian countries.
GAM has waged a guerrilla war against the government since 1976, accusing Jakarta of exploiting the resources of the province. The conflicts have claimed more than 12,000 lives, most of whom were civilians. Peace started to emerge after Aceh was hit by tsunami on Dec. 26 last year, which killed some 220,000 people.