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GAZA CITY, Gaza Strip - Israel said Friday it was close to winding up its offensive against Hamas, and the U.S. said it will provide assurances on ending weapons smuggling into Gaza as part of a ceasefire.

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

Violence was less intense on Friday with Israeli assaults killing seven Palestinians, a lower death toll than that of recent days.

"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 ceasefire 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 the Hamas rulers of Gaza won't be permitted to 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.

Mauritania heeded Mashaal's call, suspending political and economic contacts with Israel over the fighting in Gaza. Israel's embassy in Mauritania will remain and its ambassador is not being expelled.

Israel launched the 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 UN and Gaza health officials. The death toll rose by 38 on Friday, including 25 people whose bodies were unearthed from rubble and six who died of wounds from previous days, Gaza health officials said.

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

Gaza residents said they heard tanks roll away from their positions in the eastern and southern fringes of the city, leaving clouds of dust in their wake. At least 40 tanks and military vehicles retreated into Israel, but a senior security official, speaking on the condition of anonymity, said the tanks were to redeploy, and were not withdrawing.

The easing of violence gave Palestinian medics the chance to dig through rubble from recent clashes and recover 25 bodies.

Still, aircraft struck about 40 targets before dawn 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, Secretary of State Condoleezza Rice said the U.S. and Israel are signing an agreement intended to assure the Jewish state that Hamas militants will not be able to rearm if it agrees to a ceasefire in Gaza.

Rice told reporters that she and visiting Israeli Foreign Minister Tzipi Livni will sign a "memorandum of understanding" and she hoped some European countries would work out similar bilateral agreements with Israel.

"The MOU that Foreign Minister Livni and I will sign should be thought of as one of the elements of trying to bring into being a durable ceasefire, a ceasefire that can actually hold," Rice told reporters.

"As you know, there are a number of conditions that need to be obtained if a cease-fire is to be durable. ... And among them is to do something about the weapons smuggling and the potential for resupply of Hamas from other places, including from Iran," she added.

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.

Mohamed Nazzal, Hamas official from Damascus, said the Egyptians contacted his group Friday to come and hear the Israeli remarks on the Hamas propositions.

Earlier Friday, UN 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 ceasefire 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, the Israeli government spokesman, 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.

European leaders who helped raise billions of dollars in aid for Palestinians a year ago warned that fighting in Gaza could cause donors to think twice before giving again.

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 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."