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Israeli Prime Minister Ehud Olmert apologized Thursday for the deaths of Palestinian civilians in recent airstrikes, expressing "deep regret" at a summit in which he embraced and kissed Palestinian President Mahmoud Abbas.

The show of warmth came at a breakfast meeting in Jordan that was meant to help melt the increasingly icy relations between Israelis and Palestinians following Hamas militants' rise to power.

The meeting in the ancient town of Petra, sponsored by Jordan's King Abdullah II, produced promises on both sides of a more substantive meeting to come. It also brought the rare apology from Olmert, who said he felt "deep regret for the death of innocent Palestinians."

Thirteen Palestinian civilians have been killed in Israeli airstrikes in the past week, including two people slain by an errant missile Wednesday at a house in Gaza.

"It is against our policy and I am very, very sorry," Olmert said.

He did not mention a June 9 beach explosion in which another eight Palestinian civilians were killed. Palestinians blame Israel for that incident, but Israel has denied responsibility.

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Israel's air force commander, Maj. Gen. Eliezer Shakedi, said the airstrikes would continue and the rising civilian deaths were largely due to more militant activity in densely populated areas, he said.

"We have to make a great effort to try everything possible to avoid hitting civilians," he told Israel's Army Radio, adding that the airstrikes were "the most accurate and the best possible option without launching a broad and very significant (ground) operation."

After the informal get-together on the sidelines of a two-day gathering of Nobel prize winners, Olmert and Abbas pledged to meet again within weeks.

"We discussed one point -- how to prepare for a forthcoming meeting," Abbas said after returning to Ramallah. "Preparations for the meeting will begin next week," he said.

An Abbas aide, Nabil Abu Rdeneh, said the meeting would happen "in the coming two weeks," and that Abbas was awaiting word from Israel about when and where to schedule it.

Olmert and Abbas both said they had been in regular contact by telephone

Asked about his handshake with Olmert, Abbas said, "It was very warm, very warm."

Meanwhile, a family in Gaza buried the latest two civilian victims of Israeli airstrikes, receiving the bodies of Zakaria Ahmed, 45, and his pregnant sister, Fatma Abdel Khader, 35, at a neighbor's house because the family's home was too badly damaged.

The dead man was wrapped in a Palestinian flag, and his head was draped with a traditional black-and-white checkered headdress. His sister's head and body were shrouded in white and also wrapped in a Palestinian flag. Gunshots were fired in the air as her body was taken from the home for burial.

The brother and sister died when Israeli aircraft aiming Wednesday for a car carrying militants on a rocket-launching mission against southern Israel instead sent a missile into a house.

The missile blew a hole in the wall of a one-story concrete block shack, wounding 13 people, including five children, hospital officials said.

The dead man's wife was spared because she was in Gaza City with her children, mourning the death of her brother, an Islamic Jihad militant killed three weeks ago in another Israeli air attack.

The militants' near-daily rocket fire, which the airstrikes are meant to reduce, have wreaked havoc on some areas of southern Israel. Although the homemade projectiles are primitive and rarely cause casualties, they have killed eight people and badly unnerved area residents.

U.N. Secretary-General Kofi Annan called Wednesday for a halt to the Israeli pinpoint attacks, appealing to the Jewish state "to respect international law and to ensure that its actions are proportionate and do not put civilians at grave risk."

Annan's statement also urged the Palestinian Authority to do everything in its power to stop the rockets.

The Palestinian prime minister, Ismail Haniyeh of Hamas, accused Israel of ignoring Palestinian appeals for rationality.

"We are interested in calm and stability," Haniyeh said from Gaza City. "But to achieve that, the Israelis must stop the random shelling that has killed and targeted civilians."

Hamas, which is sworn to Israel's destruction, has done little to halt the rocket fire, saying it is a legitimate act of resistance, and briefly fired its own rockets after the beach explosion.

The high civilian toll is stirring debate inside Israel, with critics saying the airstrikes only inflame militant passions. Targeting militants in the crowded Gaza Strip is a particular problem during the summer, when tens of thousands of children play outside.

Since the outbreak of the latest Palestinian uprising in 2000, Israel has killed dozens of militants in missile attacks, but hundreds of bystanders have been killed and wounded.