After the meeting with Ehud Olmert, George Bush said: "The prime minister's ideas could be an important step to peace we both support."
But he added: "I believe Prime Minister Olmert agrees that a negotiated final-status agreement best serves the Israelis and the Palestinians and the cause of peace."
Olmert's "convergence" plan calls for removing remote Jewish enclaves in the occupied West Bank but keeping larger settlements forever and imposing a border if peace efforts remain frozen.
But the Israeli leader, who is on his first US visit since his election in March, says he prefers negotiations over unilateral measures, a position Bush supported at a joint news conference.
Palestinians contend the proposal would deny them a viable state envisaged in the road map peace plan sponsored by the United States, the European Union, the United Nations and Russia.
In an indirect reference to the road map, Bush said: "I appreciate the prime minister's vision of two states, two democratic states, side by side - that's possible.
"I believe Prime Minister Olmert agrees that a negotiated final-status agreement best serves the Israelis and the Palestinians and the cause of peace"
Olmert said he would exhaust all options to negotiate and reach out a hand to Mahmoud Abbas, the Palestinian president, whose Fatah faction was crushed by the Islamist group Hamas in January parliamentary elections.
"I extend my hand in peace to Mahmoud Abbas ... I will certainly meet with the elected president of the Palestinian Authority," Olmert said, adding that "it will be in the near future".
But while the Israeli leader said he accepted "the sincerity of Mahmoud Abbas", he expressed reservations about Abbas's ability to rein in fighters.
"We hope that he will have the power to be able to meet the requirements necessary for negotiations between us and the Palestinians," Olmert said.
Abbas, not Hamas
White House spokesman Tony Snow said Washington did not expect Israel to talk to Hamas.
The Islamist group refuses to renounce armed resistance and officially calls for Israel's destruction.
But Snow said the administration considered Abbas, who has a history of negotiating with Israel, the "logical person to deal with" and wanted to make sure that Olmert had "serious talks" with him.
Olmert says he will meet Abbas
in the near future
The United States and Israel say Hamas must renounce violence, recognise Israel and accept past interim peace deals if it is to be a negotiating partner.
Hamas says talks with Israel would be a waste of time.
Bush said: "I assured the prime minister that our position is steady and strong - that Hamas must change."
Olmert said Israel would make arrangements to supply humanitarian aid to the Palestinians, whose Hamas-led government is now boycotted by the United States and other Western donors.
Turning to the Iranian issue, Bush repeated a commitment to come to Israel's defence if it were attacked.