JERUSALEM, Jan. 28 - In Israel´s most significant response yet to new Palestinian policies against violence, Israel ordered its army on Friday to stop offensive operations in the Gaza Strip and scale them back sharply in the West Bank.

The army was ordered to stop arresting or killing wanted Palestinian militants unless they presented an immediate threat to Israeli lives, to lift an unspecified number of roadblocks in the West Bank to ease movement and to reopen all three crossings into the Gaza Strip.

The orders from the chief of staff, Lt. Gen. Moshe Yaalon, came hours after the Palestinian police completed their deployment throughout Gaza, charged with stopping attacks against Israeli settlers and civilians.

The developments prompted Prime Minister Ariel Sharon to remark Thursday night, "The conditions are now ripe to allow us and the Palestinians to reach a historic breakthrough in the relations between us."

General Yaalon ordered the army to halt "proactive" operations in Gaza, to allow the Palestinian security forces to redeploy "and take responsibility for the cessation of terror attacks."

Any operation to kill militants must be authorized by General Yaalon himself on the basis of "an immediate threat by active terrorist cells," or what the Israelis call "ticking bombs."

The orders go some way toward meeting the requirements of the new Palestinian president, Mahmoud Abbas, who has been trying to negotiate a longer-term cease-fire with Palestinian militant groups like Islamic Jihad and Hamas.

As a sign of the potential challenge to Mr. Abbas, Hamas did very well in municipal elections held Thursday in Gaza, reflecting popular anger at what is seen as corruption in the Palestinian Authority and widespread support for Hamas´s record of fighting the Israelis.

Both Hamas and Islamic Jihad are demanding formal Israeli agreement to a cease-fire and the release of hundreds of Palestinian prisoners - outcomes that may result from a meeting between Mr. Abbas and Mr. Sharon, which could come before mid-February, Israeli officials said.

Muhammad Dahlan, an Abbas ally who is the former chief of security in Gaza and a powerful figure in the new leadership, welcomed Israel´s announcement.

"It´s an encouraging measure that should facilitate the conclusion of a cease-fire agreement," he said. The Israeli defense minister, Shaul Mofaz, is to meet Mr. Dahlan on Sunday to coordinate security efforts and to discuss handing over responsibility to the Palestinians in some of the cities of the West Bank. It would be the first meeting at ministerial level for nearly two years.

"I have known Dahlan for 15 years," Mr. Mofaz said in London. "There is chemistry between us."

In the next few days the United States is expected to announce a coordinating committee of Israeli, Palestinian and American security officials to deal with complaints from the two sides about violations of security understandings, a senior Israeli official said Friday.

The committee would be a return to an American mediating role abandoned after the failure of the Oslo accords and the end of the Clinton administration. The idea for the committee was brought to the Israelis and Palestinians by William J. Burns, the assistant secretary of state for Near Eastern affairs, and would represent another step away from unilateral Israeli decision-making.

"Sharon realizes that if the Palestinian Authority takes these steps, he can´t miss the opportunity offered to build a better relationship," a senior Israeli official said. "This is the first time in years that the army is making a positive response to the Palestinians. We know that Arafat is gone, that Abbas is a different leader and he must be encouraged by us, and his people need to see tangible results from his election."

Mr. Sharon also recognizes that peace is popular, another Israeli official said, noting that a big demonstration against Mr. Sharon´s plan to pull settlers out of Gaza was scheduled for Monday.

"Sharon needs steps by the Palestinian Authority to convince Israelis that the settlers are wrong," the official said. "Everyone here wants this quiet to continue and is encouraged by Abbas, and doesn´t want it ruined by the settlers. Sharon sees the right wing against him, but a countertrend from the street would help him."

The American involvement, coordinated with Egypt, has been important to the latest warming, however fragile, of Israeli-Palestinian relations. The new American secretary of state, Condoleezza Rice, leaves next week for Europe, Israel and the West Bank after meeting with a Sharon adviser, Dov Weissglas, in Washington. President Bush has said he wants to see an independent Palestinian state by the time he leaves office.

The election of Mr. Abbas, who opposes violence against Israel and calls for negotiations, has given Washington more of a case to push Israel to respond to Palestinian concerns. Mr. Burns´s deputy, David M. Satterfield, said in a speech in Washington that Israel must live up to its obligations under the peace plan called the road map and cease settlement activities in the occupied territories.

He expressed satisfaction with Mr. Abbas´s actions but said Mr. Abbas must confront all those who wish to continue on the path of terrorism.

Israeli officials also urge caution, saying Mr. Sharon will insist that Mr. Abbas move to dismantle Hamas and Islamic Jihad, confiscate their weapons and destroy their rocket factories before any move toward political negotiations. Mr. Abbas wants to co-opt the militants, not fight them. So the current optimism may founder.

Still, it was a day of movement. In another Israeli gesture to Mr. Abbas, Jihad Massimi, a member of Al Aksa Martyrs Brigades and a former police commander in Nablus, was released from Israeli prison at the request of the Palestinian Authority.

Mr. Sharon is also expected to accept an army recommendation to remove two senior Palestinian security officials from Israel´s most- wanted list: Taufik Tirawi, commander of Palestinian intelligence forces in the West Bank, and Rashid Abu Shubak, who succeeded Mr. Dahlan as the head of preventive security in Gaza.

Israel is also expected to allow the resumption of deep-sea fishing off the Gaza coast.

In Gaza, Hamas won in 10 of the strip´s 25 towns and villages, winning control of seven of the local councils, including the three largest, and 77 out of the 118 seats at stake. Mr. Abbas´s Fatah faction took three councils and 39 seats, and independents won three seats. Turnout was more than 80 percent.

The vote reflects widespread support in Gaza for Hamas, which provides impoverished people there with welfare, health services, schools and kindergartens - areas in which the chaotic Palestinian Authority has failed to deliver. But a senior Israeli military official said the results were not especially important, given the influence of local clans that supported slates of candidates. The vote had more to do with local issues than national policy, the official said.

More important will be legislative elections throughout the West Bank and Gaza on July 17.

In Beit Hanun in northern Gaza on Friday, Enshira Hamad, whose husband is a Palestinian Authority policeman and whose son, Luai, 25, was killed in fighting with Israel, said she had voted for Hamas. "They are not corrupt, and there is no nepotism," she said. "They chose the path of Islam. They helped me during this intifada, financially and with food supplies. They don´t differentiate. If you are Fatah, poor and a martyr, they help you."

In December, in 26 council elections in the West Bank - which has 350 councils - Fatah won 12, Hamas won 8 and independents the rest. There will be more rounds of local elections in the coming months. (Copyright 2005 The New York Times Company 01/29/05)