The unexpected electoral success of the Salafis — reported to have won about 25 percent of the votes in the first round of the elections, second only to the roughly 40 percent for the Muslim Brotherhood’s Freedom and Justice Party — is terrifying Egyptian liberals and troubling the West. But their new clout is also presenting a challenge to the Muslim Brotherhood, in part by plunging it into a polarizing Islamist-against-Islamist debate over the application of Islamic law in Egypt’s promised democracy, a debate the Brotherhood had worked hard to avoid.

“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.”…

Every major party here — liberal or Islamist — supports retaining the clause in the Constitution stipulating that Islam is the source of Egyptian law. But competing Islamist parties offer conflicting ideas about “activating” the clause.

The most liberal — like the former Brotherhood members in the Center Party and the presidential candidate Abdel Moneim Aboul Fotouh, both breakaways from the Brotherhood — advocate essentially secular-liberal states, arguing that government should not get involved in interpreting Islam.

The Salafis, on the other hand, often favor the idea that a specialized council of religious scholars should advise the Parliament or review its legislation to ensure compliance with Islamic law.