Israeli Prime Minister Ehud Olmert expressed "great sorrow" Sunday for the airstrikes that destroyed houses in the Lebanese town of Qana and killed dozens of people, many of them children, but said he would not halt the army's operation.

The Qana attack threw efforts to broker a cease-fire in the 19 days of fighting between Israel and Hezbollah into a tailspin, and increased calls for Israel to halt its attacks. Israeli officials maintained their stance that they would only agree to a cease-fire that ended the threat of Hezbollah attacks against it.

Olmert apologized for the Israeli attack.

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"I express great sorrow in the name of the state of Israel and the army over the deaths of Lebanese civilians in Qana," Olmert said during Israel's weekly Cabinet meeting, according to a participant in the meeting. "There is nothing further from our thoughts and our interests than striking civilians. Everyone understands this. When we strike civilians, the world understands this is an exceptional case that does not represent how we act."

Qana has been used by Hezbollah guerrillas to fire hundreds of rockets at Israel, Olmert said, accusing Hezbollah guerrillas of wanting "to see children's blood, this is the only weapon they have left."

"We will not stop this battle, despite the difficult incidents this morning," Olmert said. "We will continue the activity and if necessary it will be broadened without hesitation."

The attacks early Sunday morning destroyed houses in Qana as people were sleeping inside, killing at least 50 people, many of them children.

The attacks at Qana came just five days after Israel bombed a U.N. post in southern Lebanon, killing four U.N. observers.

Army Chief of Staff Lt. Gen. Dan Halutz said the army tried to limit civilian deaths, but that was especially difficult in the fight against Hezbollah.

"A terror organization, by its nature, seeks cover among and between civilians. We are required to do everything we can to hit a minimum number of civilians. I can't promise that this is 100 percent possible," he said. "Unfortunately people who gathered in one house, and we didn't know about their presence, were struck. We regret this."

The army said it had warned the residents several days ago to leave the area because of Hezbollah activity there.

A senior air force official, speaking on condition of anonymity because he was not authorized to divulge details of the attack, said Hezbollah fighters had launched rockets from as close as 50 yards from the building that was destroyed Sunday. The official added that the villages in the area looked abandoned to the military.

"We deeply regret the loss of any civilian life and especially when you talk about children who are innocent. This is not the code of conduct of the Israeli army," said Gideon Meir, a senior Foreign Ministry official.

The violence came just over 10 years after Israel shelled a U.N. compound at Qana in April 1996, killing 91 Lebanese who had sought refuge from fighting. Israel apologized, saying that it was aimed at Hezbollah militants who were firing from nearby. A U.N. report found that the shelling was "unlikely" to have been an accident.

Furious over the latest attack Sunday, Lebanese officials canceled a planned visit to Beirut by U.S. Secretary of State Condoleezza Rice, and Prime Minister Fuad Saniora demanded an immediate and unconditional cease-fire, rejecting her efforts to negotiate a broader truce deal. Rice said she would stay in Jerusalem, adding, "We want a cease-fire as soon as possible."

Rice scheduled a new meeting with Olmert on Sunday night.

For his part, Olmert said Sunday that Israel would not rush into a cease-fire that does not remove the threat of Hezbollah attacks from its northern border and involve the creation of an international peacekeeping force to patrol south Lebanon.

"We won't end this battle, despite the tough results. This is the right thing to do. Hezbollah, like Muslim terror, threatens Western civilization," he told the Cabinet, adding that he had no plans to reduce operations in Lebanon.

The fighting began July 12 when Hezbollah fighters crossed the border into Israel and attacked an army patrol, killing three soldiers and capturing two others. Israel responded swiftly with a wide-scale air and artillery bombardment of southern Lebanon and later sent ground forces into border villages, where they fought fierce battles with the guerrillas.

Before the attack at Qana, at least 458 Lebanese were killed in the fighting, according to Lebanese officials. Thirty-three Israeli soldiers have died, and Hezbollah rocket attacks on northern Israel killed 18 civilians, the Israeli army said.

In addition to the scores of deaths in Qana, there was also heavy fighting Sunday in southern Lebanese border villages that wounded three Israeli soldiers. Hezbollah fired about 115 rockets into northern Israel, wounding six people.

A draft U.N. resolution aimed at ending the conflict called for an immediate cease-fire and the creation of an international force for south Lebanon to prevent Hezbollah from attacking Israel again.

Security officials said Sunday they believe they have a week before diplomacy forces an end to the fighting, so they are speeding up their strikes on Hezbollah to weaken the group as much as possible before that.

Meanwhile, aides to Olmert, who met with Rice late Saturday, said he did not oppose a pullout from the disputed Chebaa Farms territory on the border — a key Lebanese demand — as a gesture to strengthen Lebanon's government.

Israel kept control of Chebaa Farms when it withdrew from southern Lebanon in 2000 after an 18-year occupation. The United Nations certified that Israel had withdrawn completely and ruled that Chebaa Farms, which Israel captured in the 1967 Mideast War, was actually part of Syria. Hezbollah, which controls southern Lebanon, has pointed to Israel's presence in the disputed territory to justify its continued attacks on Israel.

Israeli opponents of a pullout worry it will be perceived as a victory for Hezbollah in the current fighting and encourage the guerrilla group, and other enemies of Israel, to step up attacks on the Jewish state.

Rice, on her second trip to the region since the violence began, presented a cease-fire package to Olmert on Saturday that included deploying more than 10,000 troops along the border area, according to senior Israeli officials. Her plan also called for Hezbollah to release the two captured Israel soldiers, and she urged Israel to withdraw from the dispute Chebaa Farms area, the Israeli officials said, speaking on condition of anonymity because they were not authorized to speak to the media.

It was not clear if the attack at Qana changed the parameters of the cease-fire proposal.