Israeli Prime Minister Ehud Olmert also said that there would be "far-reaching consequences" for the deadly rocket attack on the northern city of Haifa.
"Nothing will deter us," he said at the beginning of his government's weekly Cabinet meeting. "There will be far-reaching consequences in our relations on the northern border and in the area in general."
However, Peretz said, Israel will not reoccupy Lebanon, nor will it stay there for the long term.
On the other side, Lebanon's Cabinet issued a statement Sunday saying the country faces "real annihilation" by Israel, and accused the Jewish state of using banned weapons against Lebanese civilians.
"We are facing a real annihilation carried out by Israel," Information Minister Ghazi Aridi said after an emergency cabinet meeting.
"Israel is using internationally prohibited weapons against civilians," he said.
The Lebanese information minister did not elaborate on the weapons allegedly used. But there were Lebanese media reports, which could not be confirmed, that Israel had used phosphorus incendiary bombs and vacuum bombs, which suck up the air and collapse buildings.
Meanwhile, in a sign that diplomatic roads are not completely closed, Lebanon's government said Sunday that Italy had relayed Israeli conditions to stop its assault on Lebanon: release the two captured Israeli soldiers and pull Hezbollah back from the Israeli border.
Aridi said Italian Prime Minister Romano Prodi spoke to Lebanese Prime Minister Fuad Saniora, and relayed the conditions made by Israeli Prime Minister Ehud Olmert.
Aridi said Prodi told Saniora that "Premier Olmert has two conditions for a cease-fire: handover of the captured soldiers and Hezbollah's withdrawal beyond the Litani (River)."
He said Prodi relayed Olmert's conditions to Saniora as part of a "personal initiative."
"Nothing is official because the real negotiations have not started yet," Aridi said.
The Litani River is about 18 miles north of Israel's coastal border with Lebanon. Israel invaded Lebanon in 1978 to push Palestinian guerrillas beyond the Litani, to prevent rocket attacks on Israel's northern communities. Israel again invaded in 1982 and occupied Beirut, but withdrew gradually under guerrilla fire to a border buffer zone in 1985. That security zone was abandoned altogether in 2000.
In other developments:
Lebanon's Western-backed, anti-Syrian prime minister, Fuad Saniora, indicated Saturday night he might send his army to take control of southern Lebanon from Hezbollah guerrillas - a top U.N. demand but also a move that might risk civil war. But on Sunday, Lebanon's president, Emile Lahoud, a staunch pro-Syrian and close ally of Hezbollah, vowed that Lebanon "will not surrender" and blasted the United Nations.
CBS News has learned that an will most likely begin next week. The evacuation would be led by the USS Iwo Jima, with Marine helicopters ferrying as many as 8,000 Americans to nearby Cyprus.
Eight people were killed in the northern city of Haifa when Hezbollah rockets smashed into the city's train station. Soon after, Israeli warplanes bombarded the guerrilla group's headquarters in south Beirut again with a barrage of missiles, sending palls of smoke over the crowded residential area.
President Bush joined world leaders Sunday in urging Israel to after four days of steady bombing against its neighbor Lebanon. "Our message to Israel is, look, defend yourself but as you do so be mindful of the consequences, so we've urged restraint," Mr. Bush said.
Fears are mounting that the fight could expand across the region as Israel accused Iran and Syria - top Hezbollah backers - of supplying the guerrillas with sophisticated new missiles that hit Haifa. The Syrian government warned of an "unlimited" response if Israel attacks it. "Any aggression against Syria will be met with a firm and direct response whose timing and methods are unlimited," Information Minister Mohsen Bilal said.
Hezbollah denied it received Iranian help and Tehran said it had no role in the fighting, disputing Israeli claims that 100 Iranian soldiers had helped Hezbollah attack the Israeli warship. Iran's President Mahmoud Ahmadinejad condemned the Israeli offensive, accusing Israel of "behaving like Hitler."
In Cairo, Egypt, on Saturday, the foreign ministers of 18 Arab countries calling on the Security Council to intervene to stop the escalating crisis in the region. The Arab League declared the peace process "dead" and asked the U.N. Security Council to start negotiations from scratch.
Israeli tanks and armored personnel carriers late Saturday, Palestinian residents said, approaching a Palestinian town. The Israeli military would not officially confirm the new incursion.
As the politicians exchanged rhetoric, fighting on both sides showed no signs of subsiding.
The damage in southern Beirut - a teeming Shiite district where Hezbollah's main headquarters complex is located - was colossal after Israel unleashed its worst bombardment yet overnight, before the Haifa strike. A series of 18 explosions rocked the city before sunrise.
In an apparent retaliation, Hezbollah rockets fell on the Israeli city of Haifa, killing eight people.
Soon after, Israeli warplanes bombarded the guerrilla group's headquarters in south Beirut again with a barrage of missiles, sending palls of smoke over the crowded residential area.
The death toll continued to rise in Lebanon: Police said 130 people, almost all civilians, have died the five-day Israeli onslaught. In Israel, 23 have died, including 15 civilians killed by rocket fire.
Beirut, the capital city of 1.5 million people, was emptying as residents fled to the relative safety of the mountains and the eastern Bekaa Valley - though in the past 24 hours Israel expanded its strikes to the entire country.
Al-Manar television, Hezbollah's main voice to the world, was knocked off the air for eight minutes by the pounding. The Jiyeh power plant, on the southern outskirts, was in flames after being hit, cutting electricity to many areas in the capital and south Lebanon. Firefighters pleaded for help from residents after saying they didn't have enough water to put out the blaze.
Large swaths of the capital were covered in fine white dust from the barrage. Around the Hezbollah compound in the southern district known as Dahiyah - entire blocks were littered with heaps of rubble and twisted metal, and fires raged.
Hezbollah denied Israeli media reports that its leader, Sheik Hassan Nasrallah, had been wounded in an airstrike Sunday, the Arab and Lebanese media said.