Mr. Bush said Monday in the Oval Office that Cheney would "reassure people that the United States is committed to a vision of peace in the Middle East."
As Cheney tries to help hold together fragile negotiations between Israelis and Palestinians, Mr. Bush says he's still optimistic that a peace deal can happen before he leaves office.
Cheney departs Sunday for a trip to Oman, Saudi Arabia, Israel, the West Bank and Turkey. Oil is also on his agenda, as the White House - coping with high energy prices that have socked American consumers - continues to push for greater oil production in the Mideast.
The vice president's visit comes on the heels of a brief troubleshooting mission to the Mideast by Secretary of State Condoleezza Rice. She was able to pressure the moderate Palestinian leadership to resume peace talks with Israel, which broke off after a deadly Israeli military incursion into Gaza.
"I'm optimistic that we'll be able to achieve a vision that shows a way forward, and I'm optimistic leaders will step forward and do the hard things necessary so people don't have to live in deprivation and fear," Mr. Bush said, addressing reporters after a meeting with Polish Prime Minister Donald Tusk.
In his final year in office, Mr. Bush has turned a Mideast peace deal into a signature foreign policy goal. But violence in the Gaza Strip and southern Israel has hampered the peace talks between Israeli Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas. Cheney will meet with both men.
Palestinians have also condemned Israeli plans to build more housing in disputed east Jerusalem - an area the Palestinians hope to make the capital of a future independent state.
Mr. Bush made clear he expects Cheney to prod the leaders to stick to their obligations under the U.S.-backed road map, which calls on the Palestinians to disarm militants and for Israel to halt settlement construction. "Those obligations are clear," Mr. Bush said.
The United States blames recent violence on Hamas, which took over the Gaza Strip last July and is deemed by the U.S. to be a terrorist organization.
Without naming Hamas, Mr. Bush said: "There's one force in the Middle East - and some suspect that they're funded from outside governments and outside movements, all aiming to destabilize democracy, all aiming to prevent the vision where people can live side-by-side in peace, all wanting to destroy Israel."
Mr. Bush said the key question is whether enough will exists to reject those extremist forces.
"Our mission is exactly along those lines, and I'm optimistic," Mr. Bush said.
On Monday, Olmert instructed his army to halt airstrikes and raids into the Gaza Strip in response to a serious drop in rocket fire from the territory, allowing Egypt to proceed in its role as a mediator. Israeli defense officials and the Hamas rulers of Gaza said there was no formal truce in place.