Bush will also meet Jordan's King Abdullah II as well as Iraqi and Pakistani leaders before an address to the World Economic Forum on the Middle East.
Tzipi Livni, Israel's foreign minister, and Shimon Peres, Israel’s president, will lead the Israeli delegation to the forum.
After arriving in Egypt, Bush held talks on the peace process with Hosni Mubarak, Egypt's president.
Stalled negotiations
A day earlier, the US president met King Abdullah, Saudi Arabia's leader, in the Saudi capital, Riyadh.
King Abdullah "underlined the need for the United States to exert more efforts to prompt Israel to reach results in the negotiations with the Palestinians conducive to the establishment of an independent Palestinian state", a Saudi official said.
Bush's regional tour comes months after last year's Annapolis conference aimed at restarting the stalled Middle East peace process.
He began his tour in Israel where he addressed the Knesset [parliament]as the Jewish state marked its 60th anniversary, prompting criticism that he is not acting like an honest broker in the peace effort.
"Bush has forgotten his role as the just mediator [of the Arab-Israeli conflict] and exposed his real self in the Knesset," an editorial in the Egyptian state-owned Al-Gomhuria newspaper said.
Bush called the close relationship between the US and Israel "unbreakable", and said that Israel is facing threats by adversaries in the Middle East.
Bush met Hamid Karzai, Afghanistan's president, on Saturday and will hold talks with Barham Ahmed Saleh, Iraq's deputy prime minister, on Sunday.