Israeli Prime Minister Ariel Sharon refused to establish a timetable for withdrawing Israeli troops from Palestinian cities and towns after hours of talks with Secretary of State Colin Powell Friday.

"I hope we can find a way to come to agreement on this point of the duration of the operations and get back to a track that will lead to a political settlement because that is uppermost in everyone's mind," Powell said.

The secretary was said to be reconsidering Saturday's meeting with Yasser Arafat after a female suicide bomber on Friday blew herself up in a crowded Jerusalem market, killing six and wounding 84.

"He's looking at the whole situation in terms of the bombing and where we are," said State department spokesman Richard Boucher.

Powell had planned to tell Arafat that the time has come for action.

"What is important now is not just rhetoric going on into the air with no effect but action, action that will bring this violence under control, action that will give a feeling of hope to the people in the region and that will be my message to Chairman Arafat and we will see what his reaction is," Powell said.

On Friday, Sharon gave no commitment on when the Israeli military operation would end.

"Israel is waging war against the infrastructure of Palestinian terrorism and Israel hopes to conclude this war very soon," the prime minister said.

The two did make a "mutual commitment" to bring the Israelis and Palestinians to negotiations toward a peace settlement that would eventually lead to a Palestinian state, Powell said.

"We recognize that eventually to reach the kind of solution that is needed, the parties must talk," Powell said, "the parties must begin negotiations."

He said Sharon had offered "a commitment to peace, a commitment to finding a way forward ... so that these two peoples can live together side by side."

Foreign Minister Shimon Peres, following a separate meeting with Powell, said Israel has no interest in remaining in the Palestinian areas for any length of time. "We are talking about a week or something a little bit more than that," Peres said.

President Bush last week called on Israel to pull back "without delay." Initially supportive of Israel's counterterror tactics, the administration has accelerated its demands that Israel ease up.

In what appeared to be a gesture ahead of Powell's arrival, Israeli forces withdrew from about two dozen small towns and villages. However, they briefly moved into a new one: Kalil near the northern city of Nablus, where troops made arrests before leaving, the military said in a statement Friday. Military activity continued in a number of other cities, including Jenin, Nablus, Ramallah, Bethlehem, Dura and Dahariyah, south of Hebron.

Israel's army says 4,185 Palestinians have been detained since the operation began two weeks ago.

Sharon cast the military operation as a prudent response to terrorist attacks.

"The suicide bombers' terrorism represents a danger for Israel and the entire free world," he said. "Israel is the only democracy in the world in which there are guards in every school and in every kindergarten in order to protect the children against Palestinian terrorism."

Although Sharon offered no timetable for ending the two-week military thrust, Powell said the prime minister "is anxious to bring these operations to an end."

Powell said that while the United States recognizes the need of Israel to defend itself, "at the same time, as a friend of Israel, we have to take note of the long-term strategic consequences" of the spiraling violence.

On Saturday, Powell meets with Arafat in his devastated office in the West Bank city of Ramallah, in which Arafat will be pressed to take a tough stand against violence. Powell said this week that Israel must deal with Arafat as a partner in peacemaking.

Both Powell and Sharon stressed the enduring U.S.-Israeli relationship.

"This friendship will continue forever," said Sharon, who made a point of correcting his translator when she left off the word "forever."

Powell agreed, saying, "very important." He added: "The American people have stood by and with Israel for many years ... and it is a friendship that can never be broken."

Powell and Sharon met alone for several hours at the prime minister's residence before Israel's security cabinet joined the talks.

Later Friday, Powell was expected to take a helicopter tour of the troubled Lebanon border area. Israeli warplanes blasted suspected guerrilla hide-outs in southern Lebanon after Hezbollah fighters attacked Israeli outposts in a disputed border area.

Powell came to Israel late Thursday from four days of talks with Arab leaders, all of whom demanded Israel quit the West Bank and turn it over to Arafat for a state.

A senior U.S. official suggested in Washington that this might be Arafat's last chance to make a legitimate public attempt to stop terror against Israel. Powell intends to tell the Palestinian leader that the United States plans to cut off relations with him unless he renounces terror, said the official, speaking on condition of anonymity.

Powell earlier stopped for four hours in the Jordanian capital of Amman, where he met with King Abdullah II. The king offered Jordan's help in easing the suffering of Palestinians in the West Bank once a cease-fire is in place.

Abdullah urged Powell to increase pressure on Sharon to withdraw his troops and to accept Arafat as "the legitimate leadership and elected president of the Palestinian people," the royal palace said in a statement issued in Amman after Abdullah's meeting with Powell.

The king urged Powell to work toward a detailed peace plan setting "specific time frames" for a Palestinian state as well as ending the violence and Israeli occupation.

The Associated Press contributed to this report.