Egyptians were rallying Friday in central Cairo to demand that the ruling military council expedites the handover of power and abolishes the interim constitution that effectively tightens its grip on power, dpa reported.
The Muslim Brotherhood and several other Islamist groups are supporting the rally in Tahrir Square, the focal point of a popular uprising that forced Hosny Mubarak from power in February 2011.
The military council has granted itself sweeping legislative and executive powers in recent days, dissolving the Islamist-led lower house of parliament following a court ruling that it was unconstitutional.
It also gave military police and intelligence the authority to arrest civilians and refer them to military courts, a move seen as an attempt to revive the emergency laws that expired after three decades last month.
Hundreds of activists, many of them Islamists, have camped out in Tahrir Square to protest.
The mounting crisis between Egypt's generals and Islamists comes as Egypt awaits the official result of a hotly-disputed presidential election.
Muslim Brotherhood candidate Mohammed Morsi and the last Mubarak-era prime minister, Ahmed Shafiq, are both claiming victory.