The ruling military council had given Egyptian lawmakers a Thursday deadline to decide on the makeup of a panel tasked with drafting the country's next constitution.
The Supreme Council of the Armed Forces said Egypt would revert to the 1971 constitution, suspended after the 2011 revolution, if lawmakers didn't find a resolution.
Lawmakers early Thursday agreed to award 16 of the 39 seats set aside for political parties to the Muslim Brotherhood's Freedom and Justice Party and eight to the Salafist al-Nour Party. The rest would be divided among eight other parties, Egyptian news service al-Ahram reports.
Some lawmakers had objected to the dominance of Islamic parties on the constitutional panel. Islamists have the majority in the Egyptian Parliament, however.
Other seats would be divided among judges, religious leaders, workers' unions and revolutionary leaders.
Egypt this month is to have a runoff presidential election pitting FJP leader Mohammed Morsi against Ahmed Shafiq, the last prime minister to serve under ousted President Hosni Mubarak.