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Israel said Friday it was close to winding up its offensive against Hamas, and diplomats in Washington said the U.S. will provide assurances on ending weapons smuggling into Gaza as part of a cease-fire.

However, Hamas’ Syrian-based political chief Khaled Mashaal rejected Israeli conditions for a cease-fire and demanded an immediate opening of the besieged territory’s borders.

“I hope we are entering the end game and that our goal of sustained and durable quiet in the south is about to be attained,” Israeli government spokesman Mark Regev said.

He said it was possible that Cabinet ministers would make a decision on a cease-fire as early as this weekend. But he said Israel was first waiting to receive reports from envoys who traveled Friday to Cairo and Washington to discuss terms of a truce.

Israel wants militants to halt rocket fire and international guarantees that militants won’t rearm before it agrees to a truce.

In the Qatari capital of Doha, Hamas chief Mashaal took a tough line and asked a summit of Arab countries to back him by cutting off any ties with Israel.

“We will not accept Israel’s conditions for a cease-fire,” Mashaal told the summit. He said Hamas demands that “the aggression stop,” Israeli troops withdraw and crossings into Gaza open immediately.

Israel embarked upon an air and ground war against Gaza militants on Dec. 27 to stop the rocket fire that has traumatized southern Israel for years. But the spiraling Palestinian death toll, which includes hundreds of civilians, has drawn international outrage and touched off intense diplomatic activity to end the violence.

More than 1,100 Palestinians have been killed since the war began on Dec. 27, including 346 children, according to the U.N. and Gaza health officials. The death toll rose by three dozen on Friday, including 25 people whose bodies were unearthed from rubble, Gaza health officials said.

Thirteen Israelis have been killed, four by rocket fire, according to the military.

The Israeli military kept up pressure on Hamas Friday. Before dawn, aircraft struck about 40 targets including smuggling tunnels along the Egyptian border, a rocket launcher ready for firing and a mosque that housed a tunnel entrance and was also used to store arms, the military said.

In Washington, diplomats said the U.S. and Israel are working toward an agreement on the final working day of the Bush administration that would facilitate a cease-fire.

Secretary of State Condoleezza Rice and visiting Israeli Foreign Minister Tzipi Livni are to ink the deal on Friday. The pact also would assure Israel that additional steps will be taken to end weapons smuggling into Gaza and prevent Hamas from rearming. Diplomats say the text calls for enhanced intelligence cooperation and U.S. technical and logistical support for border monitors.

The diplomats say the hope is that the agreement will satisfy Israeli concerns about reopening Gaza border crossings and will be an important piece of an Egyptian cease-fire being negotiated in Cairo.

Earlier Friday, U.N. Secretary-General Ban Ki-moon, on a visit to the West Bank, urged Israel to declare a unilateral cease-fire in Gaza, but Israel rebuffed the idea.

“I strongly urge Israeli leadership and government to declare a cease-fire unilaterally,” Ban said from Ramallah, the seat of the West Bank government of Palestinian President Mahmoud Abbas, a fierce rival of Hamas. “It’s time to think about a unilateral cease-fire from the Israeli government.”

But Regev dismissed that idea.

“I don’t believe that there’s a logical expectation in the international community that Israel unilaterally cease fire while Hamas would continue to target cities, trying to kill our people,” he said.

Chief Israeli negotiator Amos Gilad arrived in Cairo for his second visit in two days to seek clarifications and express his views about the latest Egyptian cease-fire proposal.

An Egyptian security official, speaking on condition of anonymity due to the sensitivity of the talks, said “signs are encouraging” for a breakthrough” in negotiations over a cease-fire.

Palestinian medical officials reported an 11-year-old girl was killed in a shelling in northern Gaza and witnesses reported an airstrike on a Gaza City mosque as people were headed there for Friday prayers. The Israeli military had no comment.

Militants sent rockets flying at Israel more than 10 times, injuring three people, including one critically, officials said.

In the West Bank, Palestinian medics said Israeli soldiers shot dead a 20-year-old Palestinian during a violent protest against Israel’s Gaza Strip offensive.

Witnesses said demonstrators hurled rocks at troops who stopped them from marching into the Israeli-controlled sector of Hebron. The witnesses said the soldiers fired tear gas and rubber bullets to disperse the protesters but the man killed was hit by a live round to the head. Five other men were injured, medics said.

The army had no immediate comment.

Intense Israeli military activity in Gaza on Thursday exacted a steep price from Hamas when Interior Minister Said Siam was killed in an airstrike. Siam was the commander of Hamas security forces and was widely feared in Gaza.

A small crowd of mourners buried Siam in Gaza City on Friday. His white-shrouded body was draped in a green Hamas flag and some of the people who carried it chanted, “Greetings from Hamas!” One man fired an assault rifle in the area in a traditional salute.

Siam was seen as a main architect of the violent Hamas takeover of the Gaza Strip in June 2007, when Hamas fighters expelled forces loyal to Western-backed Palestinian President Abbas. He was the highest Hamas official killed in the offensive.

Hamas leaders went into hiding before the war began and none attended the funeral. But a statement distributed there in the name of Gaza’s Hamas prime minister, Ismail Haniyeh, said, “This new crime committed by the Zionist war machine will not affect the determination of our people or drive us to raise the flag of surrender.”

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