"Now is the time to make difficult choices," he said after a first-ever visit to the Palestinian territories, which followed meetings with Israeli leaders in Jerusalem the day before.
The president outlined U.S. expectations for the resolution of some of the hardest issues in the violent conflict, one of the world's longest-running and most intractable.
Mr. Bush said that disputed territory must be mutually negotiated, but he said "any agreement will require adjustments" to the borders drawn for Israel in the late 1940s. He was referring to Israeli neighborhoods on disputed lands that Israel would keep when an independent Palestinian state is formed.
At the same time, Mr. Bush reiterated that any viable Palestinian state must be "contiguous," saying Palestinians deserve better than a "Swiss cheese" state.
Mr. Bush offered no specifics to resolve the fact of a disputed Jerusalem, but urged both sides to work toward a solution.
"I know Jerusalem is a tough issue," Mr. Bush said.
Mr. Bush is in the Mideast for eight days, trying to bolster his goal of achieving a long-elusive Mideast peace accord by the end of his presidency.
Earlier Thursday in a joint appearance with Palestinian President Mahmoud Abbas, Mr. Bush predicted that a Mideast peace treaty would be completed by the time he leaves office. He said he's convinced that both Israeli and Palestinian leaders understand "the importance of democratic states living side by side" in peace.
"I am confident that with proper help, the state of Palestine will emerge." Mr. Bush told Abbas. "And I'm confident when it emerges, it will be a major step toward peace. I am confident that the status quo is unacceptable, Mr. President, and we want to help you."
Abbas, standing alongside Mr. Bush, called on Israel to fulfill its commitments to a Mideast peace plan, and said he hopes "this will be the year for the creation of peace."
Also Thursday, Mr. Bush named U.S. Air Force Gen. William Fraser to oversee compliance with U.S.-backed peace plan known as the "roadmap," a U.S. official said.
CBS News senior White House correspondent Bill Plante reports Mr. Bush's visit has also been met with skepticism from the Israeli public. Both sides view Olmert and Abbas as weak leaders, and the U.S. president as a lame duck.
The U.S. is perceived in the Palestinian areas as a staunch ally of Israel, at the expense of the Palestinians, but Abbas said Mr. Bush's visit "gives our people great hope," Abbas said.
President Bush stood next to Abbas during the news conference directly beneath a portrait of his late nemesis, Yasser Arafat, CBS News White House correspondent Peter Maer reports.
The picture of a grinning Arafat is positioned just to the left of the presidential podium. Arafat is buried near the Palestinian government compound where Mr. Bush conferred with Palestinian officials.
The U.S. leader always shunned any contacts with Arafat. Thursday, notes Maer, Mr. Bush was closer to the late PLO leader in death than he ever was when Arafat was alive.
Mr. Bush's three-day visit to Israel and the West Bank is geared toward showing support for renewed Israeli-Palestinian peace talks following seven years of violence.
The president said he expects both Israelis and Palestinians to "honor their obligations under the road map" peace plan, and that Israelis should help the Palestinians modernize their security forces.
The road map calls on Israel to halt settlement activity in the West Bank, while requiring the Palestinians to dismantle militant groups. Neither side has fully carried out its obligations.
"In order for there to be lasting peace, President Abbas and Prime Minister Olmert have to come together and make tough choices," Mr. Bush said. "And I'm convinced they will. And I believe it's possible - not only possible, I believe it's going to happen - that there be a signed peace treaty by the time I leave office. That's what I believe."
The president described the current round of negotiations as an opportunity to move toward a day when there will be two democracies - Israel and a Palestinian state - living alongside one another in peace. "It is in the interest not only of the Palestinians and Israelis but of the world," Mr. Bush said.
"We can stay stuck in the past, which will yield nothing good for the Palestinians in my judgment," he said. "We can chart a hopeful future."
Mr. Bush's travels through the Mideast do not include a stop in Gaza, which is controlled by the militant group Hamas, which the U.S. considers a terrorist group. The split in Palestinian governance - with Hamas controlling the Gaza Strip and Abbas controlling the West Bank - has divided the Palestinian people. Gaza and the West Bank lie on opposite sides of Israel.
Hamas has "delivered nothing but misery" to Palestinians living in Gaza, Mr. Bush said, adding that he doesn't know whether the West Bank-led government of Abbas can resolve the Palestinian division this year.
Earlier today, heavy fog in the West Bank gave President Bush an unscheduled, close-up glimpse of the frustrations faced daily by Palestinians.
Instead of taking a helicopter to his talks in Ramallah, the president was driven from Jerusalem by motorcade. At one point he passed through a security checkpoint and drove within sight of the separation barrier despised by Palestinians.
Mr. Bush later quipped that the dozens of vehicles in his motorcade made it through without being stopped. But he added, he's "not so exactly sure that's what happens to the average person."
When he was asked later about the 30-minute drive, the president acknowledged the indignities faced by Palestinians trying to get from place to place. He mentioned the case of a man held up for hours by Israeli security even though he was a Palestinian peace negotiator.
Mr. Bush noted that the checkpoints "create a sense of security for Israel," but he said "they create massive frustration for the Palestinians."