WASHINGTON - Seven weeks after the fall of Baghdad, President Bush and the leaders of Israel and the Arab world face both rewards and risks as they turn their attention from war to peace at a pair of summits near the Red Sea this week.

On his first Middle East foray since taking office, Bush will meet tomorrow at the Egyptian resort of Sharm el Sheikh with moderate Arab leaders and the new Palestinian prime minister, Mahmoud Abbas. The next day, he will move up the Gulf of Aqaba to Jordan for a second summit with Abbas, Israeli Prime Minister Ariel Sharon and King Abdullah II of Jordan.

Bush's decision to make the trip a peace mission instead of a victory lap will probably pay dividends for him in the Arab world, which felt humiliated by Iraq's rapid defeat and has seethed over U.S. support for Sharon's crackdown on Palestinian terror in the West Bank and Gaza.

Leaders of Egypt, Jordan and Saudi Arabia have long pressed Bush to exert more leadership in ending the Israeli-Palestinian conflict. They were doubtless relieved to hear Bush's remarks to Egypt's Nile TV last week: "I want them to look me in the eye so they can see that I am determined to work to make this happen."

Bush will also be keeping faith with British Prime Minister Tony Blair, who went out on a political limb in joining the U.S. invasion of Iraq and prodded Bush to make Arab-Israeli peace a top postwar priority.

With U.S. and British troops engaged in a risky, open-ended and at times violent occupation in Iraq, Bush and Blair need to show skeptics at home that the war enhanced prospects for peace in the region, as both have asserted it would.

Bush's peace mission will win plaudits for him in Europe, where many leaders viewed the Arab-Israeli conflict as a worse source of instability than Saddam Hussein and were fearful of what they viewed as an American scheme to remake the Middle East through force alone.

But the effort is not without political risk for Bush. Conservative Republicans and the Christian right, key elements of his political base, have strongly supported Sharon's tough line against Palestinian violence. They are also deeply suspicious of any peace initiative, such as the Bush-backed "road map," that has been developed by Europe, the United Nations and the State Department.

Any impression that Bush is exerting undue pressure on Israel is likely to alarm Jewish voters, possibly diminishing the major gains he has made in this overwhelmingly Democratic constituency as a result of his strong support for Israel.

Martin Indyk, the U.S. ambassador to Israel during the Clinton administration, said Bush "is going to be concerned about the Jewish community" as he heads for re-election. At a recent Brookings Institution briefing, Indyk noted polls showing that Bush could double the Jewish support he received in 2000, strengthening his position in key states such as Florida.

But Indyk said most American Jews want to see Bush "move the parties forward in a way that would end the terrorism and remove this dark cloud that hangs over Israel's future."

Deepening the bond

Sharon, by cooperating with Bush in pursuing the road map, stands to deepen the bond he believes they have formed in their joint campaign against terror and Islamic extremism. Such a bond is a major political asset in Israel. Two of his Likud predecessors, Yitzhak Shamir and Benjamin Netanyahu, suffered politically when they ran afoul of the White House.

Sharon echoed Bush last week in using the loaded word "occupation," which implies holding ground belonging to someone else, to describe the Israeli military presence in the West Bank and Gaza. His remark "was calculated to show the Americans that he is willing to take some heat to be a team player," said Jon B. Alterman, director of Middle East studies at the Center for Strategic and International Studies.

Sharon also sees a reduction of violence as key to rescuing the Israeli economy, which is reeling from the loss of tourism and investment. "Sharon is going through a maturation process and beginning to digest the bitter truth that he cannot eradicate terror and improve the economic situation without a political solution," commentator Yoel Marcus wrote in the Israeli newspaper Haaretz.

At the same time, Sharon "doesn't want to be the Thanksgiving turkey at a U.S.-Arab rapprochement summit," Alterman said. And Sharon has to worry about losing support on the political right. His "occupation" comment drew protests from members of his Likud Party. Jewish settlers, whose cause he has long championed and whose communities are at risk, are gearing up for a major fight.

Like Sharon, the new Palestinian prime minister faces gain and political peril from collaborating with the United States.

Bush has hailed Abbas as a reformer while trying to sideline Yasser Arafat, who was not invited to either summit. But Arafat remains the man recognized throughout the Arab world as the Palestinians' leader and retains enough political power to constrain Abbas' actions.