"So that at some point in time, the Palestinians who agree that Israel ought to exist and agree that the state ought to live side-by-side with Israel in peace have something to be for."Final status issues
Before the visit, Olmert and Abbas met and agreed to start talking about the hardest issues in a future peace deal, including borders, security and a division of Jerusalem.
Mark Regev, the Israeli government spokesman, said that the two leaders authorised their negotiators "to conduct direct and ongoing negotiations on all the final status issues".
Saeb Erekat, the senior Palestinian negotiator, said Tuesday's meeting was "serious and in depth". He confirmed that the two leaders told their aides to begin talking about core issues.
"The president urged that the year of 2008 be a year of peace," he said.
The peace negotiations - which were effectively restarted at a conference in Annapolis, Maryland, in November - have stalled over Israeli plans to build new homes in east Jerusalem and demands that Abbas does more to rein in Palestinian fighters.
At least one member of the Islamic Jihad was killed when an Israeli missile was fired at a building in the northern Gaza Strip just hours before Bush was due in Israel.
An Israeli army spokeswoman said the military had carried out "an attack on a rocket-launching cell in Beit Lahiya" after it had fired several projectiles into Israel.
Condoleezza Rice, the US secretary of state, is be accompanying Bush. She suggested Israelis and the Palestinians should quickly.
"We do expect both sides to act with urgency. We do expect the negotiations to move forward, we do expect both sides to live up to their obligations," she said in an interview with Israel's Channel 10 TV.
"The Palestinians need to do everything they can to fight terror. Israel frankly needs to look at its road map obligations and to do nothing that would prejudge the final status agreement."Gaza Strip protests
Bush's trip will also include visits to Kuwait, Bahrain, the United Arab Emirates, Saudi Arabia, and Egypt.
However, the Hamas-controlled Gaza Strip will be noticeably absent from the tour, with the US considering the group a terrorist organisation and refusing to negotiate with its leaders.
Hamas is organising another anti-Bush rally on Wednesday, with a four-metre-long banner denouncing Bush as a "war criminal" serving as the centrepiece.
Sami Abu Zuhri, a Hamas spokesman, said: "Hamas and the Palestinian people do not expect a single thing from this visit, considering American policies completely favour the Israelis,"
On Tuesday, about 3,000 supporters of the Islamic Jihad marched in the Gaza Strip, chanting: "Bush, you are the great devil."
The protesters also shouted "Death to America", "Death to Israel", and burned American and Israeli flags.
US snipers will take up positions on rooftops and entire districts will be sealed off in Jerusalem and and the West Bank city of Ramallah as Bush visits.
An American member of al-Qaeda has called for the US president to be greeted "not with flowers and applause, but with bombs".
The ongoing animosity between Tehran and Washington is threatening to overshadow to tour after the Pentagon reported that Iranian speedboats swarmed around US vessels in the Straits of Hormuz, threatening to blow them up.
"I am there to reassure and to look people in the eye and say, I believe Iran is a threat; we have a strategy to deal with it; and we want to work with you," Bush told the Al-Arabiya news channel.
Mohammad Ali Hosseini, Iran's foreign ministry spokesman, said that the visit smacked of "interference" and "propaganda".
However, Dana Perino, a White House spokeswoman, said Iran "is certainly not the main reason for the trip".
"The main reason for the trip is to advance these negotiations and make sure that those are on the right track, as well as to talk about the president's commitment to the region."