Israeli air force jets bombed the house of a senior Hizbullah official in southern Lebanon. Reports said that at least 13 people were killed in the attack. This came after Hizbullah's rockets killed eight Israelis in Haifa.
The death toll in the four-day-old conflict rose above 100 in Lebanon, and stood at 24 in Israel.
Hizbullah said it had used "Raad (Thunder) 2 and Raad 3" rockets against Haifa. A senior political source said Israel's army chief, Dan Halutz, had told a cabinet meeting "Some of the missiles were probably produced by Syria."
Meanwhile, Israel raised the alert level in Tel Aviv, about 130 km south of Lebanon, in what the army said was a precaution. Halutz has said Hizbollah has rockets with a range of 70 km and possibly longer.
On her part, US Secretary of State Condoleezza Rice said on Sunday the United States was deeply concerned about mounting civilian casualties in Lebanon but that an immediate ceasefire would not solve the problem.
Rice said U.S. officials were weighing hour-by-hour whether Americans in Lebanon should leave. "We obviously have plans and contingency plans should we need to bring people out," she told reporters at a Group of Eight summit in Russia.
Rice backed Israel's right to retaliate for Hizbullah attacks. "It's obvious that when you have rockets being fired into your territory ... that there is a responsibility of Israelis to defend their people. I don't think you can ask any less of any state," she said, according to Reuters.
But she said she had told Olmert "we are deeply concerned about the effect on innocent civilians and we would hope that Israel would be mindful of and restrained in its operations so that innocent civilians do not suffer".
Rice said the cease-fire demanded by Lebanese Prime Minister Fouad Siniora would not work. "What we really need is to concentrate on a way forward that is going to permit the cessation of violence which first of all will be sustainable, that we won't be back three weeks from now talking about getting another cessation of violence," Rice said.