Mr Bush (left) is hoping for a peace deal by the year's end
US President George W Bush has repeated his commitment to a lasting Middle East peace deal after meeting Palestinian leader Mahmoud Abbas in Egypt.
Mr Bush also met Egyptian President Hosni Mubarak, who questioned him about a controversial speech he made in Israel, and Afghan leader Hamid Karzai.
Israeli PM Ehud Olmert is not there but has sent his defence minister.
A BBC correspondent says there is little hope for the peace deal Mr Bush wants by the time he leaves office.
"It breaks my heart to see the vast potential of the Palestinian people, really, wasted," the Associated Press quoted Mr Bush as saying.
Standing next to Mr Abbas in the Red Sea resort, he added: "It would be an opportunity to end the suffering that takes place in the Palestinian territories."
Mr Bush is due to meet the leaders of Iraq, Jordan and Pakistan over the weekend, which takes in a World Economic Forum.
The BBC's Christian Fraser says Mr Bush will spend his visit trying to balance the support he has shown the Israelis during the past week with his country's wider strategic interests in the Arab World.
Mr Bush is due to address the World Economic Forum on Sunday
Mr Bush received a warm welcome from his Egyptian counterpart but among those gathered there is little confidence that the meetings will result in any significant progress, our correspondent says.
An editorial in Egypt's main state-owned newspaper, al-Ahram, said the Israeli-Palestinian peace process was effectively over under Mr Bush, and criticised him for hardly referring to the Palestinians during his keynote speech in Israel.
Mr Mubarak "wanted to make sure that my approach toward the Middle Eastern peace is firm", Mr Bush said.
He insisted: "I believe we can get a state defined by the end of my presidency, and we'll work hard to achieve that objective."
Israeli Defence Minister Ehud Barak is expected to press again for the release of the captured Israeli soldier, Gilad Shalit, as a condition of any truce with Hamas, the militant group which controls the Gaza Strip.
Mr Bush's previous stop was in Saudi Arabia, where he had a request turned down for a big increase in oil production to help reduce world prices.
Speaking in Egypt, he said recent Saudi output rises would be a help but would not solve America's problems.
"Those who are screaming the loudest for increased production from Saudi Arabia are the very same people who are fighting the fiercest against domestic exploration, against the development of nuclear power and against expanding refining capacity..." Mr Bush said.
"We've got to do more at home. And we need a Congress who will be responsive to those requests."