On Friday, he and British Prime Minister Tony Blair vowed to mobilise international support to help make it happen in the post-Yasir Arafat period.
"I'd like to see it done in four years," said Bush, elected last week to a second four-year term. "I think it is possible."
Bush and Blair said Arafat's death offered an opportunity. As an immediate goal they pledged to help the Palestinians hold elections within the next 60 days to choose a new president to replace Arafat.
At a joint White House news conference after their talks, Blair said he and Bush would work to mobilise international support to help bolster institutions for a viable Palestinian state.
He cited the need to revive the Palestinian economy, build up its security institutions and its government to fight corruption, and reform the political system.
"What we will do is anything that is necessary to make this strategy work," said Blair.
At the same time, Bush announced he would travel to Europe soon after he beginning his new term early next year to stress that he wants to work together with European allies on the Middle East and other issues.
"What we will do is anything that is necessary to make this strategy work"
British Prime Minister Tony Blair
Much of Europe was in an uproar over the US-led invasion of Iraq and Bush was attacked on the campaign trail by Democratic candidate John Kerry for souring ties with traditional allies.
Bush said he would use the trip "to remind people that the world is better off, America is better off, Europe is better off when we work together".
Aides said the itinerary was uncertain but the trip would likely be in February and that one stop would be to Brussels for European Union and Nato talks.