CAIRO — As it prepares to take power in Egypt, the Muslim Brotherhood is overhauling its relations with the two main Palestinian factions in an effort to put new pressure on Israel for an independent Palestinian state.

Officials of the Brotherhood, Egypt’s dominant Islamist movement, are pressing its militant Palestinian offshoot, Hamas, which controls Gaza, to make new compromises with Fatah, the Western-backed Palestinian leadership that has committed to peace with Israel and runs the West Bank.

The intervention in the Palestinian issue is the clearest indication yet that as it moves into a position of authority, the Brotherhood, the largest vote getter in Egypt’s parliamentary elections, intends to both moderate its positions on foreign policy and reconfigure Egypt’s.

Brotherhood officials say that they are pulling back from their previous embrace of Hamas and its commitment to armed struggle against Israel in order to open new channels of communications with Fatah, which the Brotherhood had previously denounced for collaborating with Israel and accused of selling out the Palestinian cause. Brotherhood leaders argue that if they persuade the Palestinians to work together with a newly assertive Egypt, they will have far more success forcing Israel to bargain in earnest over the terms of statehood.

“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.”

Already, Mr. Fahmy claimed, the Brotherhood’s new stance was making “a fundamental difference,” including jump-starting the stalled reconciliation talks between the two Palestinian groups.

The Brotherhood’s supreme guide, Mohammed Badie — effectively its chairman — had personally told Hamas’s top political leader, Khaled Meshaal, to be “more flexible,” Mr. Fahmy said, and at recent talks in Doha, Qatar, Hamas had agreed for the first time to let Fatah’s leader, Mahmoud Abbas, preside over the first six months of a unity government for the Palestinian territories until new elections could be held.

“Hamas never would have accepted that Abbas heads the government,” Mr. Fahmy said, “but now they are.”

Moussa Abu Marzook, a senior Hamas leader who has settled in Cairo after fleeing Damascus, said that the group was full of hope about the rise of the Brotherhood, from which Hamas originally sprang 25 years ago.

His circumstances attested to those hopes. In 1995, he was arrested the United States, and spent two years fighting an Israeli extradition request and until recently was permitted to enter Egypt only under the watchful eye of its intelligence service. Now he spoke from the large and sunny salon of the second-floor office above his well-fortified suburban villa here. He acknowledged that the rise of its fellow Islamists in Egypt had set off a deep debate inside Hamas.

Some argued against any compromise with Fatah, predicting that Hamas’s bargaining position would only grow stronger as its Islamist allies in Egypt took on new power. Fatah, on the other hand, had lost its primary regional sponsor, the government of Mr. Mubarak.

But Mr. Abu Marzook said that those who expected the new Egypt to back Hamas completely would be disappointed. “It’s normal that the Muslim Brotherhood will be more realistic than they used to be when they weren’t in power,” he said.

He said he favored more conciliations with Fatah. “Reaching reconciliation is in the best interest of the Palestinian people,” he said.

Fatah officials, for their part, say that so far they have been pleased with the Brotherhood’s neutral approach to both factions. “The Muslim Brotherhood in Egypt is doing everything it can to end the Palestinian division,” said Saeb Erekat, Fatah’s chief negotiator.

Mr. Fahmy said that the Brotherhood still believed that United Nations resolutions still qualified Hamas’s armed struggle as a legitimate movement of resistance to an armed occupation. “The texts of all religions guarantee the right to self-defense,” he said.

But he said that the Brotherhood’s support would never extend to supplying weapons. “Foolishness,” he said. “Turning the region into an arms market is not good for anyone. We are against the distribution of weapons anywhere or supporting such a movement, even if we are biased towards it in defending people’s rights. We are careful about the region’s stability.”

Fatah has gone much further than both Hamas and the Brotherhood in seeking peaceful coexistence with Israel. But Mr. Erekat suggested that the differences between the parties may not be as great now as they were in the past. “The Muslim Brothers are the majority party now in Egypt; they are the masters of themselves,” he said. “If they think it’s in the best interest of Egypt, let them abolish the Camp David treaty. But this isn’t what I heard.”

Israel, for its part, rejects the 1967 borders as insufficiently defensible for its security.

But some in Israel are watching the shifts. “Hamas is showing indications that it’s moving towards a more responsible position,” said Shlomo Brom, an analyst and retired brigadier general in the Israeli military. “But because of Hamas’s bloody history, it will be very difficult for the Israeli government to accept this reality. I don’t know how long it will take.”

Mr. Fahmy, though, predicted continued “tranquillity” between Hamas and Israel, in part because Hamas understands that the Brotherhood needs to stability to manage Egypt’s political transition.

“Hamas considers the Muslim Brotherhood a strategic extension of itself,” he said. “And I think that this in itself is a strong guarantee that the situation will not explode in the area.”