With the departure of Secretary of State Condoleezza Rice from the Mideast, Israel resumed its bombings of Beirut. A series of at least four heavy blasts were heard in Beirut, the first Israeli strikes in the city in nearly two days. A grey cloud billowed up from the capital's southern district, a Hezbollah stronghold that has been heavily bombarded.
The afternoon strikes were the first since Sunday evening.
An official with the U.S. Central Command, which is in charge of operations in Lebanon, says the Israelis believe there are 1,000 hard core Hezbollah and 2-3,000 part-time fighters that still have to be rooted out of southern Lebanon, reports CBS News national security correspondent David Martin. They expect it to take another two weeks.
More than 424 people have been reported killed in Lebanon and Israel since fighting broke out July 12 between Israeli forces and Hezbollah guerrillas.
In other developments:
Israeli military said it had killed at least 40 Hezbollah guerrillas in what it calls the "capital of terror" in southern Lebanon, Bint Jbeil. Armored brigade commander Col. Amnon Eshel Assulin, told the Jerusalem Post that the operation proves the army's ability to reach any location in Lebanon, even Beirut, if Israel decides to enter the Lebanese capital.
A 15-year-old girl in the Arab town of Maghar was killed and at least 23 others were injured by a Hezbollah rocket, while at least five people were injured in Haifa, one seriously and two moderately. One rocket hit a bus, but only the driver was aboard at the time. One Haifa man died of a heart attack after a rocket landed near his home, medics said. Israel Radio said the man was running toward a bomb shelter when he collapsed.
Most shops and businesses in Haifa remain closed, reports CBS News correspondent Robert Berger.
Rockets also hit the towns of Kiryat Shemona, Nahariya, Tiberias, Acre and Safed.
Israel claimed its planes had destroyed the Katyusha launcher that had fired Tuesday's rockets at Haifa.
Rice, leading the first high-level U.S. diplomatic mission since war broke out in Lebanon, said Tuesday the time has come for a new Middle East and an urgent end to the violence hanging over the region.
"I have no doubt there are those who wish to strangle a democratic and sovereign Lebanon in its crib," Rice said. "We, of course, also urgently want to end the violence."
Standing beside Israeli Prime Minister Ehud Olmert as they prepared to meet in his office, Rice reiterated the United States position that a cessation of hostilities in Lebanon must come with conditions that make an enduring peace. She said she has "no desire" to be back in weeks or months after terrorists find another way to disrupt any potential cease fire.
Olmert welcomed Rice warmly and vowed that "Israel is determined to carry on this fight against Hezbollah." He said his government "will not hesitate to take severe measures against those who are aiming thousands of rockets and missiles against innocent civilians for the sole purpose of killing them."
Later, Olmert told a group of new immigrants from France that Israel has the stamina for a long fight and is determined to defeat Hezbollah.
After meeting with Palestinian President Mahmoud Abbas later Tuesday, Rice said, "We need to get to a sustainable peace, there must be a way for people to reconcile their differences."
Rice, who has disappointed some U.S. allies with her support of Israel, also met Tuesday with Peretz. Rice made no public remarks after her meetings with Olmert and Peretz.
But Peretz said Israel still has U.S. support, reports CBS News correspondent Dan Raviv.
"We want to defend our citizens, and we have broad international support ... We have no desire to open a war against Syria," Peretz said.
Syria's military is at its highest state of alert in recent years, Israel's intelligence chief told a parliamentary committee, but it's a defensive mode. Major General Amos Yadlin said "neither Syria nor Israel are interested in a military clash," but Hezbollah would like to involve Syria.
The Bush administration has said it wants to address the overall threat from Hezbollah, a Shiite militia in Lebanon, by creating conditions that will give the weak Lebanese government control over its entire territory, including south Lebanon, which is under Hezbollah control.
In a brazen July 12 raid into northern Israel, Hezbollah killed eight Israeli soldiers and captured two others, provoking Israel's biggest military campaign against Lebanon in 24 years. Hezbollah has fired hundreds of rockets at northern Israeli communities.
Israeli forces have been hammering Gaza to the south since shortly after the June 25 capture of an Israeli soldier by militants linked to Hamas group. The subsequent turmoil has highlighted the weakness of Abbas, a moderate whose Fatah party lost parliamentary elections to Hamas in January.
Both Hamas and Hezbollah have said the two attacks were not connected. Israel has responded with force on both fronts. The U.S. has insisted it will not support an immediate cease-fire if the conditions behind the fighting aren't addressed.
"Clearly, in the Arab world, one of the reactions is growing hostility to Israel and to the United States, and that reinforces essentially what is already out there," Richard Haass, president of the Council on Foreign Relations, said on CBS News' The Early Show. "The other reaction in the Arab world is to me in some ways interesting and less familiar and that is the resentment of Hezbollah. We're seeing a real split in the Arab world between the Sunni Muslims and those more aligned with the Shia."