NABATIYEH, Lebanon (AP) – Israeli troops sealed off a Hezbollah stronghold and warplanes killed six people in a market city in southern Lebanon on Tuesday, while Beirut was pounded by new airstrikes. Guerrillas fired rockets at northern Israel, killing a girl, as the two-week-old crisis showed no signs of letting up, despite frantic diplomatic efforts.

At least four heavy blasts were heard in Beirut, the first Israeli strikes in the city in nearly two days. A gray cloud rose from the capital’s southern district, a Hezbollah stronghold that has been heavily bombarded. Nearly daily pounding halted during Secretary of State Condoleezza Rice’s visit Monday.

Al-Jazeera said 20 Israeli rockets hit the Dahiyah neighborhood. The Israeli army said it hit 10 buildings housing Hezbollah personnel but did not elaborate.

Outlining the scope of the Israeli campaign for the first time, a senior army commander said Israel would only encircle Lebanese towns and villages near the border and did not plan a deeper push into the country.

“The intention is to deal with the Hezbollah infrastructure that is within reach,” Col. Hemi Livni, who commands troops in the western sector of southern Lebanon, told Israel Army Radio. “That means in southern Lebanon, not going beyond that.”

President Bush expressed concern for the civilians killed and harmed by Israeli bombs, but stopped short of calling for an immediate cease-fire that might not last.

“I support a sustainable cease-fire that will bring about an end to violence,” Bush said.

Rice, in Israel on the second leg of a Middle East tour, maintained the Bush administration’s position that a cease-fire must come with conditions that make an enduring peace for the region.

“I have no doubt there are those who wish to strangle a democratic and sovereign Lebanon in its crib,” Rice said before meeting with Israeli Prime Minister Ehud Olmert in Jerusalem. “We, of course, also urgently want to end the violence.”

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.”

Rice also met with Palestinian Prime Minister Mahmoud Abbas and told him the U.S. has not forgotten the Palestinians’ plight. At a meeting that included about a dozen U.S. and Palestinian officials, but no Hamas representatives, Rice and Abbas talked about getting additional aid to the debt-laden Palestinian government as well as the status of an Israeli soldier captured last month by Hamas-linked militants.

Olmert later said Israel has the “stamina for a long struggle” and is determined to defeat the Islamic militant group.

Meanwhile, a senior Hezbollah official said the group did not expect Israel to react so strongly to its capture of two Israeli soldiers in a July 12 raid, saying it expected “the usual, limited response.”

Mahmoud Komati, the deputy chief of the Hezbollah politburo, also told The Associated Press that his group will not lay down its arms.

“The truth is _ let me say this clearly _ we didn’t even expect (this) response … that (Israel) would exploit this operation for this big war against us,” Komati said.

Past Israeli reponses included sending commandos into Lebanon and kidnapping Hezbollah officials or briefly targeting its strongholds, he said.

The violence looked likely to drag on with tough ground fighting as Israeli forces try to move village to village near the border, facing well-armed, determined militants who have been digging in for years.

The U.S., which is pushing for the deployment of international and Lebanese troops in southern Lebanon to stop Hezbollah attacks on Israel, has angered many allies with its support of Israel and resistance to calls for an immediate cease-fire.

Arabs will insist on an immediate cease-fire and for the Lebanese government to take control over the militant Hezbollah at an international meeting in Rome on Wednesday, Jordanian Foreign Minister Abdul-Illah al-Khatib said.

German Defense Minister Franz Josef Jung said a cease-fire must be in place before any international troops are sent to Lebanon. Israel has suggested it would accept an international force _ preferably from NATO _ to ensure the peace in southern Lebanon, but Jung said after meeting his French and Polish counterparts that it was too early to say if the alliance, or a European Union force, could be put in place.

A top Hamas official in Syria said Israeli soldiers held by Hamas and Hezbollah will only be released as part of a prisoner swap.

The official, Mohammad Nazal, also raised the possibility of joining with Hezbollah to negotiate terms that would lead to the release of Palestinian and Lebanese prisoners in Israel in exchange for the three Israeli soldiers _ two held by Hezbollah and one by Hamas.

An unknown number of Americans were feared stranded in the heart of Lebanon’s war zone, where they were staying with relatives for the summer. While one evacuation organizer had said there were 300, the U.S. Embassy suggested there might be more but had no hard figures.

At least 15 Americans arrived Tuesday in the southern city of Tyre in an 80-vehicle convoy from Yaroun, a village in southeastern Lebanon, evacuation officials said.

The Orient Queen, a cruise ship under contract to the U.S. government, left Beirut on Tuesday with 393 Americans, and it will return Wednesday for the last scheduled evacuation of U.S. citizens, officials said.

At the front Tuesday, an Israeli military official said troops had surrounded Bint Jbail, a town that has symbolic importance to Hezbollah as one of the centers of resistance to the Israeli occupation 1982-2000.

Israeli forces have seized some houses on the outskirts of the hilltop town since beginning the assault Monday, but do not yet control Bint Jbail, the official said, speaking on condition of anonymity as a press statement had not been issued.

Up to 200 Hezbollah guerrillas are believed to be defending the town, which lies about 2 1/2 miles north of the Israeli border. Hezbollah’s Al-Manar TV reported the fighters were mounting a strong defense against elite Israeli troops who were trying to advance under “heavy bombardment.”

In a pre-dawn raid, Israeli warplanes destroyed two neighboring houses in Nabatiyeh, which lies 16 miles north of Bint Jbail and has been heavily bombarded.

In one house, a man and his wife and their son were killed, said the couple’s daughter, Shireen Hamza, who survived. Three men died in the other house, she said.

While buried under the rubble for 15 minutes, “I just kept screaming, telling my parents to stay alive until help comes,” she said. “My father kept saying to me in a weak voice, ‘Shireen, stay awake. Don’t sleep.'”

Security officials said seven people were killed. But Nabatiyeh Hospital received only six bodies, said Dr. Marwan Ghandour.

At least 70 rockets were fired at northern Israel, and a teenage girl was killed and three other people were injured in the Arab town of Maghar.

One rocket fired at the Israeli port city of Haifa hit a bus, another hit a house and two reportedly struck close to a hospital, injuring five people, witnesses and doctors said. One man died of a heart attack while running to a shelter, Israel Radio said.

Rockets also hit the towns of Kiryat Shemona, Nahariya, Tiberias, Acre and Safed.

Israeli Vice Premier Shimon Peres appealed to the Lebanese people to disarm Hezbollah, and he spoke of seeing “the tough scenes from Lebanon, of your women and children fleeing these days on roads that lead to the unknown.”

“As soon as the war ends, you will find in us what we really are, pursuers of peace, seekers of peace, seekers of hope,” Peres said. “There is not any conflict between Israel and Lebanon.”

Israeli Brig. Gen. Ido Nehushtan also said Israel has destroyed 100-150 rocket launchers, adding that he couldn’t say how many of Hezbollah’s approximately 12,000 rockets have been destroyed. He also said “dozens” of Hezbollah fighters have been killed.

Komati said 25 of its fighters had been killed as of Monday, and the group said two more died in ground fighting Tuesday _ raising the previously announced toll of 11.

Despite estimates of the number of Hezbollah militants that Israel claims were killed and the number that Hezbollah asserts were killed, there was no way to accurately determine the number or often distinguish between civilians and fighters.

The Lebanese Health Ministry said 369 civilians have been killed, not including the six people who died in Tuesday’s airstrike. Twenty soldiers also have died in the fighting, and the 27 reported Hezbollah deaths brought the total to 422. The increase was due to wounded who died in the hospital.

Israel’s death toll stands at 42, including 24 soldiers and 18 civilians, most killed by hundreds of rockets fired by Hezbollah.

Humanitarian efforts continued, and Olmert said Israel will allow the opening of safe passages for transporting aid to all areas of Lebanon.