"I'm looking forward to continuing our serious dialogue with you and the president of the Palestinian Authority to see whether or not peace is possible," Bush said to Olmert.
Palestinian President Mahmoud Abbas was scheduled to meet with the U.S. president later in the day.
"I'm optimistic," Bush said.
Arab countries have agreed to participate in the Middle East peace forum in Annapolis, U.S. on November 27 in a bid to achieve progress on the question of Palestinian statehood, urging the U.S. to also include the issue of Israeli-occupied Golan Heights on the conference agenda.
The leaders of Egypt, Jordan and the Palestinian National Authority, who met on Thursday to coordinate approaches for the U.S.-sponsored conference, also said they were optimistic.
President Hosni Mubarak held separate meetings with Mahmoud Abbas and King Abdullah II of Jordan in the Red Sea resort town of Sharm el-Sheikh.
Abbas had earlier urged the Arab countries "not to miss a historic chance and attend the forum."
Arab leaders previously expressed doubts over the conference, demanding a more specific agenda and questioning whether it would be effective given the current outbreak of violence in the region.
The Palestinians want a detailed agreement specifying each party's commitment concerning key points, such as future borders, the status of Jerusalem, Palestinian refugees, and Israeli settlements. Israel is looking for a more general guideline.
Israel is also seeking to retain control over East Jerusalem and key settlements in the West Bank as part of an eventual agreement.
Israeli Prime Minister Ehud Olmert said on Tuesday, following a meeting with the Egyptian president, that he expected a final peace deal to be signed with the Palestinians in 2008, shortly after the peace conference in the U.S.
