Secretary of State Colin Powell seeks Yasser Arafat's assurance of a reduction in violence and Israel's commitment to a broader West Bank withdrawal at the conclusion of his Mideast peace mission.

"I think we are making progress and are looking forward to making more progress in the next 24 hours," Powell said Tuesday.

But Israeli forces began new incursions into a West Bank town and three villages near Jerusalem, imposing curfews as part of a high security alert timed to Israel's Independence Day.

Palestinians condemned the movements. But Powell has tempered his public calls for a total and quick military departure now that Israeli Prime Minister Ariel Sharon has announced a pullout from all but Ramallah and Bethlehem within a week.

In any event, Israeli officials said the withdrawal would not preclude efforts to arrest Fuad Shobaki, whom they accused of overseeing attacks on Israel and the abortive shipment of 50 tons of Iranian weapons to the Palestinians.

And, the officials said on condition of anonymity, they remained determined to arrest the plotters of the assassination last October of Tourism Minister Rehavam Zeevi.

Powell will have a second and final session with Arafat on Wednesday at his rocket-battered Ramallah headquarters, where the Palestinian leader has been confined by Israeli troops for nearly three weeks.

In his meeting with Arafat, and in a one-hour session Tuesday with Sharon at the prime minister's home in midtown Jerusalem, Powell also was taking up the international peace conference that is quickly taking shape.

He would like to wind up the trip with Arafat's commitment to some sort of cease-fire. But Powell is falling short of the formal cease-fire he left Washington in search of 10 days ago.

Still, the peace conference would implement Powell's declared search for an accelerated political process, one that President Bush and Powell have said must produce a Palestinian state.

Bush also had insisted on a quick withdrawal of Israeli forces, echoing European and Arab demands.

Sharon said the peace conference probably would be held in June in the United States. A site has not been selected. A potential problem is that Sharon wants to screen out Arafat but attend himself, even though the tentative plan is to hold it at the foreign ministers level.

Sharon's spokesman, Raanan Gissin, said a peace conference was not a certainty. "The Americans think this is very important," he said.

Israel, Egypt, Jordan, Saudi Arabia and perhaps Morocco were possible participants, Sharon told Israel TV. An alternative is to have the Arab League represent the Arabs and possibly invite the European Union and Russia. The United States would be represented as well.

The topic may come up when Powell stops on his way home Wednesday in Cairo, Egypt, for a meeting with President Hosni Mubarak.

While Powell has steered clear of a formal cease-fire that would be considered broken with every hostile incident, he said he was working on something like it without a "specific term." In his last Mideast mission nearly a year ago, Powell called for seven days of quiet before getting back to the negotiating table — a requirement that proved impossible.

The focus of the last stage of Powell's trip is how to stop the fighting and how to pin down Israeli-Palestinian security arrangements to maintain calm in the West Bank, Israeli officials said.

Israel wants assurances from the Palestinians they would assert control, but the Palestinians say the Israeli incursion has crippled their security apparatus. Israel's response is that there are enough Palestinian security forces to get the job done.

U.S. and Palestinian officials were holding "good conversations," Powell said. However, they failed to agree on a statement condemning suicide bombings as well as calling for an Israeli withdrawal from West Bank areas, said a senior Palestinian official.

The United States objected to a Palestinian addition "calling for an end to Israel's occupation, for the establishment of the state of Palestine in the June 4, 1967, borders, with east Jerusalem as its capital, and a just solution for the refugee problem, with the needed mechanism to guarantee the implementation within an agreed timeline." That plan also would have asked additional action by the U.N. Security Council.

In Washington, presidential spokesman Ari Fleischer said Powell is exploring avenues to create an environment in which political negotiations can begin. White House officials said privately that Powell's reports to Bush had become slightly more optimistic.

The Associated Press contributed to this report.