Ban Ki-moon, the UN Secretary General, is also visiting the region and held talks with Hosni Mubarak, the Egyptian president, on Saturday.
"It is necessary for the international community to encourage this ongoing peace process," Ban said after the talks, on his first tour of the Middle East since taking office in January.
|Ban Ki-moon is set to meet the|
Palestinian president [AP]
The UN chief urged the newly formed Palestinian unity government to meet demands set by Western powers.
Ban has said he will not be meeting Ismail Haniya, the Hamas prime minister of the coalition administration.
He is set to meet Mahmoud Abbas, the Palestinian president and non-Hamas members of the government.
Analysts have argued that a revived peace process is unlikely, given divisions among the Palestinians and the political weakness of Ehud Olmert, the Israeli Prime Minister, leaving both sides ill-equipped to negotiate.
Olmert has refused to talk to the new Hamas-led Palestinian national unity government because it has not recognised Israel and renounced violence.
Rice stops first in Aswan, Egypt, for talks with the foreign ministers of the 'Arab quartet' - Egypt, Jordan, Saudi Arabia and the United Arab Emirates - and with Hosni Mubarak, the Egyptian president.
The meeting with Mubarak comes amid controversial constitutional changes being pushed by his government which have been criticised by the US.
Egyptians are set to vote on the changes, which the opposition has said could Egypt into a police state, in a referendum on Monday.
"I'm really concerned about it," Rice said.
"The Egyptians set certain expectations themselves about what this referendum would achieve and the hope that this would be a process that gave voice to all Egyptians," she said.
"I think there's some danger that that hope is not going to be met."
The opposition has said it will boycott Monday's vote.
Rice is also expected to meet Olmert, Abbas and Jordan's King Abdullah.
Despite making her third trip to the region this year, Rice faces doubts about Washington's commitment to peace in the region.
"I think they are serious about putting more effort in," said Jon Alterman of the Centre for Strategic and International Studies think-tank.
"I think they are not serious about putting in the kind of effort and presidential involvement that a final settlement will require."
There are also questions in the region about whether US diplomacy is motivated more by Washington's need for Arab support to help stabilise Iraq rather than by a desire to try to resolve the Arab-Israeli conflict.