A White House spokesman said Bush joined a pre-arranged meeting between Peres and national security adviser Condoleezza Rice to reinforce the U.S. demand that Israeli forces withdraw from an incursion into Palestinian areas known as Zone A.
Bush reminded Peres of the United States' continued support for Israel and said Israel had "no better friend in the world" than Washington. But, the president said, Israel must withdraw.
The White House spokesman said he could not confirm whether the two men discussed the Israeli charge that the United States was catering to Arab interests in order to build its anti-terrorism coalition.
Bush said the U.S. war on terrorism would serve other nations.
Peres told reporters after the meeting that it was cordial, but he reiterated his answer to the same request by Secretary of State Colin Powell. Earlier, Peres said, "The secretary knows that we would like to have an immediate withdrawal. I think the secretary understands that the minute the Palestinians take the necessary steps, this may happen."
Israel wants the killers of Israeli Tourism Minister Rehavem Zeevi arrested and turned over to Israeli authorities. Zeevi was killed last week by Palestinian gunmen at a hotel in Jerusalem.
Bush extended his condolences to Peres over Zeevi's death and said he urged Palestinian Authority President Yasser Arafat to arrest the perpetrators. He told Peres that he had told Arafat that the Palestinian leader must be "100 percent" involved in ending terrorist acts emerging from the Palestinian areas.
Powell also has a meeting scheduled with Peres Tuesday. On Monday, the State Department said it had been made "quite clear" to Israel that it must act to restore calm.
"Israeli incursions into Palestinian-controlled areas have contributed to a significant escalation and tension and violence, as I noted earlier," said Deputy State Department spokesman Philip Reeker during a Monday briefing with reporters. "The government of Israel has told us that it does not intend to remain in those areas. Israeli defense forces should be withdrawn immediately from all Palestinian-controlled areas and no further such incursions should be made."
Bush has said he would support a Palestinian state once a peace agreement had been forged between Israel and the Palestinians.