“Now we have to deal with the Palestinian parties as an umbrella for both of them, and we have to stand at an equal distance from each,” said Reda Fahmy, a Brotherhood leader who oversees its Palestinian relations and is now chairman of the Arab affairs committee in Egypt’s upper house of Parliament. “Any movement of the size of the Muslim Brotherhood, when it is in the opposition it is one thing and then when it comes to power it is something completely different.”

The shift in the Brotherhood’s stance toward neutrality between Hamas and Fatah — acknowledged by officials of both groups — may relieve United States policy makers, who have long worried about the Brotherhood’s relationship with the more militant Hamas. The United States considers the Palestinian group to be a terrorist organization. But the shift in Egypt’s policies may unnerve Israel, because it is a move away from former President Hosni Mubarak’s exclusive support for the Western-backed Fatah movement and its commitment to the peace process. Israeli officials have said they will not negotiate with a Palestinian government that includes Hamas.

But Mr. Fahmy said the Brotherhood believed that Palestinian unity could break the deadlock in talks with Israel. “A Palestinian negotiator will go the table and know that all the Palestinian people are supporting his project,” Mr. Fahmy said. “This will be a huge change and very important to both sides.” Jailed at times by the Mubarak government for his role in the Brotherhood, Mr. Fahmy spoke this month from an ornate hall of Parliament.

After decades of denunciations and enmity — Brotherhood texts still sometimes refer to the Jewish state as “the Zionist entity” — Brotherhood leaders have said that as members of the governing party they will honor Egypt’s 1979 peace accord with Israel. Some of its leaders say they believe that such coexistence can become a model for Hamas as well, if Israel moves toward accepting a fully independent Palestinian state.

He noted that Hamas had already made statements indicating that it would accept coexistence with Israel along its borders before the 1967 war. “It is true that it is like a person who is forced to drink poison or eat a dead animal, but they still made the statements,” he said, “so we support that, provided that this state within the ’67 borders is completely sovereign in air and in sea and in land.”