She was due to hold talks with Palestinian President Mahmoud Abbas around 4:00 pm (1400 GMT) in the West Bank city of Ramallah before heading to Jerusalem for a private dinner with Israeli Prime Minister Ehud Olmert.
On Thursday, Rice will meet with her Israeli counterpart Tzippi Livni and defense minister Amir Peretz in Jerusalem.
She flew in from Egypt, a key US ally who has been a major player in trying to bring Israel and the Palestinians back to the negotiating table. There she urged Palestinians to form a government that will respect principles set out by world powers in an effort to relaunch the stalled peace process.
"The Palestinians need a government that can represent the interests of the Palestinian people," she said Tuesday night. "They need a government that can engage the international community and can engage the broad consensus that a two-state solution is the answer.
"We talked about how to help [Palestinian President Mahmoud Abbas] in terms of a Palestinian government and a Palestinian authority that is fully committed to the Quartet principles," she said of her meetings with Egyptian officials and ministers from the Gulf Cooperation Council.
The Middle East quartet - the European Union, Russia, United Nations, and United States - drafted the so-called road map that envisions an independent Palestinian state living side by side in peace with Israel.
But after the radical Islamist Hamas movement formed a government last March, the West withheld all direct financial aid to the Palestinian Authority over Hamas' refusal to recognize the Jewish state, renounce violence, and respect previous agreements with Israel.
Ahead of Rice's visit, a cabinet minister from Prime Minister Ehud Olmert's Kadima party said that Israel should accept a Saudi peace plan adopted by the Arab League in 2002.
"We should take the bull by the horns and, when I say that, I mean we should accept the moderate [Arab] countries' initiative, the Saudi initiative," justice and housing minister Meir Sheetrit told public radio.
He said that Israel would be willing to withdraw from Arab territory occupied since the 1967 Middle East war, as stipulated in the Saudi blueprint, in exchange for a "complete peace."
"If we are talking about overall peace, if we want overall peace, we are compelled to accept all the elements of the initiative and withdraw to the 1967 borders.
"We should invite Abu Mazen [Abbas] for face to face talks," he said, emphasizing that Israel was "ready to make significant compromises to draw its permanent borders."
Recent reports in Israel - denied in Riyadh - have mentioned secret talks between Israeli and Saudi officials, with Olmert leaving it understood that he had met a member of the kingdom's royal family.
But last week, Olmert said that the Saudi initiative did not constitute a basis for negotiations.
Rice arrived in Cairo for talks with "moderate" Arab counterparts after kicking off a regional tour in Saudi Arabia with an appeal for an end to Palestinian infighting.
There had been mounting press speculation in Egypt that the group would declare a new coalition against Iran, whose drive for nuclear power is described by Washington as a cover for acquiring atomic weapons.
"This is not a new coalition by any stretch of the imagination," Rice said. "This is a group of states that have a lot of answers to the problems of the Middle East ... that wants to promote an environment in which extremism and terrorism are fought and fought vigorously."
US President George W. Bush called last month for Rice to travel to the region "to engage moderate leaders ... to help the Palestinians reform their security services, and support Israeli and Palestinian leaders in their efforts to come together to resolve their differences."
Rice also expressed her "great concern" over fighting between Palestinian factions loyal to Hamas and supporters of Abbas' Fatah party.
The worst violence in the territories since Hamas came to power erupted at the weekend after the movement tried to prevent Fatah loyalists from protesting over non-payment of salaries, which they have not received in full since March.
Abbas and Hamas Prime Minister Ismail Haniya are engaged in tortuous efforts to form a national unity cabinet with the aim of lifting the Western aid freeze.
© 2006 Agence France-Presse
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