The Al Nour party, widely regarded two years ago as bumbling amateurs, now has unique leverage. It was the only Islamist party to support removing Mr. Morsi, despite his ties to the more moderate Islamists of the Muslim Brotherhood. And the sight of Al Nour’s bearded sheik, standing behind the general who announced the takeover on television, was the only signal to Egyptian voters that the move had not been an attack on Islam, as some of the ousted president’s supporters are saying.

The party played a starring role in the military’s choreographed presentation of its takeover as the chance to reunify a country on the brink of civil war between opponents and supporters of Mr. Morsi’s Muslim Brotherhood. But while Al Nour’s leaders say they intend to build bridges, some liberals say the party is pushing potentially divisive demands, from picking a new prime minister to keeping Islam prominent in any new constitution…

The party’s ability to block Mr. ElBaradei from the premiership raised new alarms from liberals about what the ultraconservatives, known as Salafis, might demand next, even after the expulsion of the more moderate Brotherhood.

“This stage of the revolution was against this type of Islamist party,” said Shady el-Ghazaly Harb, one of the organizers of the anti-Morsi protests. “We will not have any concessions when it comes to writing the constitution, and we will die for that,” he added, vowing that the charter should include “a separation of religion and politics, because parties should not be built on religion.”