Mr Bush made the remarks at a joint news conference with Mr Olmert following talks on peace prospects, which have been hindered by the election of the militant group Hamas to the new Palestinian leadership.
Mr Olmert campaigned for the premiership on a platform of fixing Israel's borders by 2010 with or without the Palestinians, and Mr Bush said: "the prime minister's ideas could be an important step toward the peace we both want."
But the US president underscored that any settlement "will only be achieved on ... a mutually achieved basis. And no party should prejudice the negotiations on a final status agreement."
The talks are the first meeting between the two since Mr Olmert became prime minister.
Mr Olmert said his country is committed to the international roadmap to Middle East peace, but that it could not wait "indefinitely for the Palestinians to change".
He added he would meet with Palestinian leader Mahmoud Abbas in the "near
future" and praised Mr Abbas as "genuine" and "sincere" in his desire to
settle the Israeli-Palestinian conflict.
But he said the rise of Hamas "severely undermines the possibility of promoting a genuine peace process."
Success of talks crucial
Before the meeting, White House spokesman Tony Snow said: "This is a chance to get to know each other better, but also roll up their sleeves and talk about the best ways to move forward ... so that we can try to create the conditions for peace in the region.”
The success of the summit is seen in Israel as a key barometer for the future of Mr Olmert's government, formed last month, which will require full US support for implementing its ambitious plan.
Mr Olmert will attempt to emulate the warm ties established between Mr Bush and his mentor Ariel Sharon, who won crucial US backing before he withdrew Israeli settlers and troops from the Gaza Strip last year.
"Olmert will try to build a strong relationship with the president and continue in the Bush-Sharon tradition," a spokesman for the Israeli embassy in Washington, David Segal, said.
Mr Olmert knows the same trust between Israel and its chief ally will be essential to carry out the proposed second withdrawal from the West Bank, several times more complex and fraught with difficulties.
Under his plan, Israel will withdraw tens of thousands of settlers from the West Bank in order to fix its borders. In turn, Israel will retain several settlement blocks housing some 200,000 Jews in Palestinian areas.
But while Mr Olmert is ready to move unilaterally, the United States continues to view the "roadmap" -- an internationally sponsored peace plan which calls for a negotiated Israel-Palestinian settlement -- as the only viable solution to end the Middle East conflict.
No far-reaching decisions
But despite the week-long preparations for the summit, officials on both sides have made it clear in recent days that Mr Bush and Mr Olmert did not anticipate announcing any far-reaching decisions.
"We are not ready to jump to final status negotiations," Mr Snow said.
Mr Olmert said US efforts to take action against Iran's nuclear programme the UN Security Council are of crucial importance because Iran is a threat to the international community.
Mr Bush stressed US resolve to protect Israel against any possible threat from Iran.
Mr Olmert will deliver a speech on Wednesday (local time) before a joint session of Congress.