JERUSALEM (Reuters) - Israel will sharply reduce its military operations in the West Bank and Gaza Strip in response to efforts by Palestinian President Mahmoud Abbas to end attacks on Israelis.

The new rules of engagement, issued soon after Palestinian paramilitary police widened their control in the Gaza Strip, put limits on so-called assassinations of militants and appeared aimed at boosting Abbas, who hopes to revive peacemaking.

But in a sign of challenges for Abbas, unofficial results showed the Islamic militant group Hamas swept nearly two-thirds of the seats in Gaza Strip council elections seen as a test of strength between Hamas and Abbas.

An Israeli military communique on Friday said: "Proactive army operations in the Gaza Strip will cease in the areas in which Palestinian security forces have redeployed."

It said "army targeting of terrorists in the West Bank will take place only if there is an immediate threat by active terrorist cells" and only with explicit authorization from the chief of staff.

The statement said army chief Moshe Yaalon had decided on the moves "in light of the ongoing cooperation between Israel and the representatives of the Palestinian Authority."

Arrangements would be made, the army said, to reopen next week Gaza border crossings closed after a series of attacks by gunmen.

Responding to the Israeli announcement, Palestinian cabinet minister Saeb Erekat called on Israel to declare a full cessation of violence against Palestinians.

"We have a similar obligation to stop violence against Israelis anywhere in line with the ´road map´," he said about a U.S.-backed peace plan charting mutual steps toward creation of a Palestinian state alongside a secure Israel.

PALESTINIAN POLICE DEPLOY IN S. GAZA

Building on a northern Gaza deployment a week ago, some 2,000 Palestinian paramilitary police fanned out across the southern part of the occupied territory, which they have not patrolled since 2001.

The United States and Israel have demanded the Palestinians crack down on militant attacks on Israelis before peacemaking can move forward.

Over the past week, violence has dropped sharply in the Gaza Strip, where Abbas is trying to coax militants into a cease-fire in the run- up to a planned Israeli withdrawal this summer.

With Palestinian flags flapping from their vehicles, paramilitary police drove in a convoy to Gaza´s border with Egypt, where Israel has mounted punishing raids in residential areas to root out weapons- smuggling tunnels and gunmen.

Other contingents armed with assault rifles took up positions between Jewish settlements on occupied land, frequently hit by mortar bombs and rockets fired by militants, and Palestinian towns.

"I am very happy. Now we can sleep in peace," said Salah al-Najar, who lives near the Jewish settlement of Morag. "My children were constantly afraid of noises Israeli tanks made."

Israeli Prime Minister Ariel Sharon said on Thursday conditions were right for a "historic breakthrough" on peace after measures taken by Abbas, including reaffirmation of a long-standing weapons ban for civilians, to bring calm.

President Bush, in an interview published on Friday in The New York Times, said Abbas had shown strength in the early phases of his administration.

"He is sending assurances that he will put a 100-percent effort into protecting the people on both sides of the issue from terrorists. And to me, that´s an impressive start," Bush said.

In a sign of a new push for peace after Yasser Arafat´s death, U.S. officials said Secretary of State Condoleezza Rice would visit the region early next month. Palestinian officials said she would hold talks in Israel and the West Bank on Feb. 6 and 7. (Additional reporting by Allyn Fisher-Ilan in Jerusalem and Wafa Amr in Ramallah) (© Reuters 2005 01/28/05)