Palestinian ruling party Hamas has denounced the US president's support for Israeli plans to unilaterally redraw its borders if peace talks fail.
A Hamas spokesman said it would spell the end for the Palestinian cause.
George W Bush described Israel's plan as "bold" after talks with Israeli PM Ehud Olmert, but urged him to pursue direct talks with the Palestinians.
Hamas, branded a terror group by the US, Israel, and the EU, won elections in January and formed a government.
Mr Olmert is proposing the withdrawal of tens of thousands of Israelis from isolated settlements in the West Bank while, at the same time, consolidating other settlements housing hundreds of thousands of others.
Palestinians see the Israeli plan as a land grab of territory captured by Israel in 1967 and have condemned it.
Speaking in Washington on Tuesday, Mr Olmert said he would exhaust all bilateral options before going it alone to set Israel's final borders, but reiterated that he would not negotiate with Hamas.
Hamas does not recognise Israel and has rejected calls for a permanent end to violence.
The Palestinians say Mr Olmert's plan would leave them without enough land to establish a viable state and accuse him of not being serious about negotiations.
Mr Olmert is holding a series of meeting with Bush administration members in Washington and will address the US Congress at 1100 (1500 GMT).
After meeting his Israeli counterpart on Tuesday, Mr Bush said he believed a negotiated settlement could still be reached between Israel and Palestinian Authority President Mahmoud Abbas.
"I believe, and Prime Minister Olmert agrees, that a negotiated final status agreement best serves both the Israelis and the Palestinians and the cause of peace," he said.
The US president made a distinction between Mr Abbas, who he said "speaks out for peace", and Hamas "who does not".
Mr Bush said a settlement should be based on the establishment of two states living side-by-side, as envisioned in the 2002 roadmap peace plan.
But he added: "Today, Prime Minister Olmert shared with me some of his ideas. I would call them bold ideas... [which] could be an important step toward the peace we both support."
Mr Olmert made what appeared to be a significant concession by saying he would try to pursue talks with Mr Abbas, the BBC's Justin Webb reports.
The meeting in Washington was the first between the two leaders since Mr Olmert won the election in March.