Jerusalem ? Secretary of State Colin Powell and Israeli Prime Minister Ariel Sharon emerged from hours of talks Friday with no timetable for withdrawing Israeli troops from Palestinian cities and towns on the West Bank.

“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.

Sharon, for his part, gave no commitment on when the 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.

Powell said he and Sharon had a “mutual commitment” to bring the two sides to negotiations toward a peace settlement that would eventually lead to a Palestinian state.

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

Powell said he came away from his conversations with Sharon with “a commitment to peace, a commitment to finding a way forward … so that these two peoples can live together side by side.”

Powell’s visit with Sharon will be followed Saturday by talks with Palestinian leader Yasser 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.

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 did not commit to a timetable for ending the two-week military operation in Palestinian towns and villages, Powell said he was pleased that 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.

Both men 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. 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. Israeli artillery shelled suspected guerrilla positions nearby. Hezbollah guerrillas said their mortar shells and rockets scored direct hits.

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. Europeans are almost as adamant in their demands, and some, like Germany, are beginning to punish Israel economically.

The Bush administration, initially supportive of Israel’s counterterror tactics, has muted its criticism of Arafat and accelerated its demands that Israel ease up.

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, who offered Jordan’s help in easing the suffering of Palestinians in the West Bank once a cease-fire is in place.

“People are dying. People are suffering,” the king told CNN. He said he offered Powell his kingdom’s support in his peace mission, which he called “a make-it or break-it trip.”

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 two-hour 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.