RAMALLAH, West Bank (CNN) -- U.S. President George W. Bush met with Palestinian leaders in the West Bank on Thursday, predicting that a Middle East peace treaty would be signed by the time he leaves office in 2009.

Speaking at a joint news conference with Palestinian President Mahmoud Abbas -- and a day after meeting with Israeli Prime Minister Ehud Olmert -- Bush said both men realize the importance of democratic states living together in peace.

"In order for there to be lasting peace, President Abbas and Prime Minister Olmert have to come together and make tough choices and I'm convinced they will," Bush said in Ramallah.

Abbas called on Israel to complete the terms of the road map, a U.S.-supported peace plan agreed upon in 2003. Under the road map, Israel must halt West Bank settlement activity and Palestinians must dismantle militant groups.

"We are fully satisfied with the outcome that we reached through this visit with President Bush," said Abbas. The Palestinian leader said talks touched on "all topics" and that "all the issues are in agreement. "In the coming few days, we are going to have bilateral negotiations with Israelis."

Bush said he heard "the urgency in the voice of both the prime minister of Israel and the president of the Palestinian Authority. Is it going to be hard work? You bet."

Bush said he's "confident that with proper help, the state of Palestine will emerge."

Both Abbas and Olmert agreed to work toward such an agreement at the November 27 U.S.-sponsored peace summit in Annapolis, Maryland.

During his first visit to the region as president Bush has said he hopes his presence will push the Israeli and Palestinian leaders ahead on the stalled process.

"Nudge the process forward -- pressure -- be a pain, if I need to be a pain," Bush responded when asked what he could do to break the deadlock.

"We can help influence the process and will," he said, but he added that Abbas and Olmert will have to do the "hard work."

Possibly in protest of Bush's visit to the region, Palestinian militants in Gaza stepped up their ongoing rocket and mortar assault on southern Israel on Wednesday. None of the attacks resulted in casualties, but three Palestinians died after Israel's military struck back at northern Gaza.

In response to the U.S. leader's visit, the Hamas leadership in Gaza organized protest rallies, complete with anti-Bush placards.

Speaking at Wednesday's news conference, Olmert warned Abbas that he must get control of Gaza before any peace deal can be reached.

"There will be no peace unless terror is stopped and terror will have to be stopped everywhere," the Israeli leader said.

"Gaza must be part of the package," he said. "As long as there is terror from Gaza, it would be very, very hard to reach any understanding between Israel and the Palestinians."

Hamas forces seized control of Gaza in June in what Abbas has called a coup against forces loyal to his Fatah movement. Fatah has consolidated its power in the West Bank, and the Palestinian leadership remains split between the two territories.

At Thursday's news conference, Bush called the Hamas-Fatah split "competing visions" for the Palestinian people.

Hamas has "delivered nothing but misery" in Gaza, Bush said, but added he was confident a unified Palestinian state would emerge.

A major challenge for Bush's mission has been keeping the trip focused on Israeli-Palestinian peace while other issues -- Iran, Pakistan, Iraq and soaring oil prices -- dominate the media headlines and serve as reminders of the region's instability.

Bush's visit to the region has prompted the largest security operation in Israel since Pope John Paul II's visit in March 2000. More than 10,000 Israeli police are deployed across the region to back U.S. federal officers.

Large parts of Jerusalem and much of the West Bank, including Ramallah, in effect have been shut down.

After his visit to Israel and the West Bank, Bush will depart Jerusalem on Friday for Kuwait. He will then head to Bahrain, the United Arab Emirates, Saudi Arabia and Egypt. He returns to Washington next Wednesday.