Embarking on a crucial Middle East mission, Secretary of State Colin Powell said Sunday that Israel's leader has "taken very much to heart" President Bush's call for an immediate withdrawal from Palestinian areas.

But Powell said the Prime Minister Ariel Sharon has yet to set a timetable for a pullback and Bush has not demanded one. "The president doesn't give orders to a sovereign prime minister of another country," Powell said.

Powell will see Sharon in Jerusalem late this week after stops expected in Morocco, Egypt, Spain, and Jordan for talks with Arab and European leaders.

He said he would meet with Yasser Arafat "if circumstances permit" — depending on security, access and the meeting agenda. Israel has confined Arafat to his Ramallah compound. Failure to meet with the Palestinian leader would doom Powell's efforts, Arab officials say.

Powell said he will seek a cease-fire as a first step toward a peace agreement.

"Until the violence goes down hopefully to zero, but at least to a level where you can see that both sides are acting in a responsible way and trying to cooperate in a cease-fire, you're not going to get to a peace agreement," he said on NBC's Meet the Press.

Following Bush's call for a withdrawal "without delay," Israel said it would expedite its mission aimed at rooting out Palestinian militants responsible for suicide attacks. Fighting continued Sunday in the West Bank cities of Jenin and Nablus. Defense Minister Binyamin Ben-Eliezer acknowledged U.S. pressure. "Our hourglass is running out," he said in a statement.

Powell said he spoke with Sharon on Sunday and is confident Bush's call for a withdrawal "will not be ignored."

"I know that he is trying to move the operation forward as quickly as possible. And we'll see what happens in the next couple of days," he said.

Powell said Israel's offensive has succeeded in suppressing terrorist attacks — perhaps at a long-term cost. "We may well be radicalizing a new generation, many more terrorists waiting to act once this incursion is over," he said on Fox News Sunday.

The secretary said Israel could destroy advances it has made in relations with Arab states. In his trip, Powell will call on those states to take a bigger role in pressuring Arafat to fight terrorism and to stop their own inflammatory rhetoric.

"We need more responsible statements coming out of Arab capitals," he said. "We need all Arab leaders to act responsibly in this time of crisis."

At Powell's first stop, Morocco, he planned meetings Monday with King Mohammed VI and Saudi Crown Prince Abdullah. He then heads to Egypt to see President Hosni Mubarak, and to Spain for talks with U.N. Secretary-General Kofi Annan, Russian Foreign Minister Igor Ivanov and European leaders.

Jordanian Foreign Minister Marwan Muasher said on CBS' Face the Nation that Arabs "are ready to do everything in their power to move the peace process forward." But he said "it would be really absurd to meet with all the parties to the conflict without meeting with Yasser Arafat."

Amr Moussa, secretary-general of the League of Arab Nations, told ABC's This Week that if Powell does not meet with Arafat "I don't think he'll find any other interlocutor among the Palestinians and the mission will fail."

Powell repeated Bush administration complaints that Arafat has not done enough to reach a cease-fire by speaking out against violence and using his security forces to prevent terrorist attacks. But he acknowledged that Arafat represents the Palestinian people. He noted that he talked to him as recently as April 1 and has met with him three times. U.S. envoy Anthony Zinni also met with Arafat last week.

"Chairman Arafat, whether one likes it or not and whether one approves of it or not, does occupy a position in Palestinian society. He is seen by the Palestinian people as their leader, and that has to be taken into account," Powell said.

Asked how he would measure success in his trip, Powell tried to diminish expectations for "a completely satisfactory solution" in a week's time.

"But if we have brought the violence down, if we have started to create a dialogue again between the two sides, then my trip will have been worth the energy that I'm going to put into it and the effort we're going to put into it," he said.