The 133 petitioners include academics, former officials, journalists and activists, participant Ahmed Mansoor told CNN.
The petition is addressed to Sheik Khalifa bin Zayed Al Nahyan, president of the federation, and the Supreme Council of the seven emirates in the U.A.E.
The group also wants the advisory Federal National Council to get legislative powers.
"The group called for a comprehensive reform of the parliamentary system of the Federal National Council, and included demands for free elections by all citizens," Mansoor said. "It also demanded reform of legislation governing the work of the Parliament to include legislative and monitoring authorities and calling for necessary constitutional amendments to ensure that."
There have been no public demonstrations in the U.A.E. so far. They are not officially banned, but police never grant permits for them.