In a photographic session later Tuesday, Bush said he told Peres that the United States was "saddened by the fact that a Cabinet minister was assassinated" and called the killing of Tourism Minister Rehavem Zeevi "unacceptable behavior."
Zeevi was killed last week by Palestinian gunmen at a hotel in Jerusalem.
Bush said the United States "continued to call upon" Palestinian Authority President Yasser Arafat to "to do everything he can to bring the killer to justice. It's very important that he arrest the person who did this, or those who did this act and continue to arrest those who would disrupt and harm Israeli citizens."
After the meeting, Peres told reporters that withdrawal of forces is Israel's intention "the minute the Palestinians will take over in their own hands the introduction of law and tranquility, and put in jail the main troublemakers." He said then Israel would "be more than happy to redeploy our army to their previous positions."
Peres said he was hopeful that Arafat would comply and noted that in his experience the "Palestinian Authority is very sensitive to the American and the European reaction."
A White House spokesman said Bush joined a prearranged 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 Area A.
Secretary of State Colin Powell also had a meeting 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 Israeli defense forces should be withdrawn immediately from all Palestinian-controlled areas and no further such incursions should be made."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.
Israeli leaders were mixed in their reaction to Bush's call.
Deputy Defense Minister Dalia Rabin-Pelossof said she expected the withdrawal "not in months and not even in weeks."
Others were more flexible.
"From the very beginning there was no intention to stay (in those areas), but to detain the terrorists. That is why we are there -- until we do so," the Prime Minister's media adviser, Raanan Gissin, told United Press International.
Three members of the inner Diplomatic-Security Cabinet Tuesday night agreed Israel should not give its tanks an immediate order to withdraw.
Science Matan Vilnay said in a televised debate Israel ought to "exhaust the (current) move and get out." Asked how soon the Israelis should leave, Vilnai said: "Immediately -- no. Soon, yes."
Justice Minister Meir Sheetrit said the United States was applying a double standard. Alluding to the attacks in Afghanistan he said, "Whatever the Americans may do to protect Americans in New York, we may do to protect Israeli citizens in Jerusalem."
Former Foreign Minister Shlomo Ben Ami suggested Israel might have to wait a bit to safe face.
"Tactically it should not leave outright, but should get out within a few days," he said.
The objection to a pullback came from the hawkish Public Security Minister Uzi Landau who said that a withdrawal "under U.S. pressure would be a sweeping victory for Yasser Arafat."
"The IDF ought to stay there and carry out its tasks until it fully completes them ... there comes the time where you have to defend your own citizens," Landau added.
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