“The Salafis want to have that conversation right now, and the Brotherhood doesn’t,” said Shadi Hamid, a researcher with the Brookings Doha Center, a Brookings Institution project in Qatar. “The Brotherhood is not interested in talking about Islamic law right now because they have other priorities that are more important. But the Salafis are going to insist on putting religion in the forefront of the debate, and that will be very difficult for the Brotherhood to ignore.”

The Brotherhood, the venerable group that virtually invented the Islamist movement eight decades ago, is at its core a middle-class missionary institution, led not by religious scholars but by doctors, lawyers and professionals. It has long sought to move Egypt toward a more orthodox Islamic society from the bottom up, one person and family at a time. After a long struggle in the shadows of the rule of President Hosni Mubarak, its leaders have sought to avoid potentially divisive conversations about the details of Islamic law that might set off alarms about an Islamist takeover. But their evasiveness on the subject has played into long-term suspicions of even fellow Islamists that they are too concerned with their own power.

The Salafis are political newcomers, directed by religious leaders who favor long beards in imitation of the Prophet Muhammad. Many frown on the mixing of the sexes, refusing to shake hands with women let alone condoning any sort of political activity by them. Although their parties are required to include female candidates, they usually print pictures of flowers instead of the women’s faces on campaign posters. And while the Salafis’ ideology strikes many Egyptians as extreme and anachronistic, their sheiks command built-in networks of devoted followers, and even voters who disagree with their puritanical doctrine often credit the Salafis with integrity and authenticity.

After the first election results last week, the Brotherhood’s Freedom and Justice Party quickly declared that it had no plans to form any coalition with the Salafis, with some members already ending months of restrained silence by striking back. In an interview after the vote, for example, Dina Zakaria, a spokeswoman for the party, derided the Salafis’ prohibition on women in leadership roles and their refusal to print the faces of their female candidates.

“We don’t hold stagnant positions,” she said, insisting that the Brotherhood’s party favored an evolving understanding of Islam that supported the right of women to choose their own roles. (At campaign rallies, women from the party sometimes underscore the point by saying Muhammad even enlisted women in combat.)