The Israeli attacks in south Lebanon alone killed 26 civilians and wounded dozens more, Lebanese security officials said.
A family of 10 and another family of seven were killed in their homes in the village of Dweir near Nabatiyeh.
Israel's Cabinet held an emergency meeting that decided to respond forcefully to Hezbollah's cross-border raid yesterday when its guerrillas captured two Israeli soldiers and demanded a prisoner exchange.
Israel said it had imposed a naval blockade of Lebanese ports - which Lebanese officials confirmed - and Israeli fighter bombers carried out their biggest offensive in Lebanon since Israel's 1982 invasion.
Giving the rationale to Israel Radio, Israeli Agriculture Minister Shalom Simchon said: "The government wants to change the rules of the game in Lebanon and make the Lebanese government understand that it is responsible for what happens in Lebanon."
Israeli Defence Minister Amir Peretz said his forces would in future not allow Hezbollah guerrillas to occupy positions along the southern Lebanese border.
"We will not enable Hezbollah to return" to its positions near the border, Peretz said.
Peretz demanded that Lebanese army forces be deployed along the border. Lebanon has long refused to do this, saying that it is not in business of protecting Israel's northern border.
Yesterday, the Lebanese government said it did not know of the Hezbollah operation, did not condone it and bore no responsibility for it. The Cabinet, which includes two Hezbollah ministers, urged the UN Security Council to intervene.
In a strike in the southern suburbs of the capital Beirut, an Israeli missile hit the building housing the studios of Hezbollah's Al-Manar TV in Haret Hreik district this morning, said the channel's press officer Ibrahim Farhat. He had no details, but the station's manager Abdullah Kassir told Voice of Lebanon radio that one person was hurt.
The station continued to broadcast, reporting that an Israeli rocket had hit a "minor transmission unit".
Israeli helicopter gunships and jet fighters scoured southern Lebanon for guerrillas launching rockets into northern Israel.
Hezbollah announced it was firing rockets at the Israeli town of Nahariya, and said that in some of its attacks it was using a rocket called "Thunder 1" for the first time. The missile appeared to be more advanced than the inaccurate Katyusha which has been the standard Hezbollah rocket for years.
Israeli warplanes also struck deep inside Lebanon, striking a civic centre attached to a Shiite Muslim mosque near the town of Baalbek in eastern Lebanon, a Hezbollah stronghold.
The witnesses also said Israeli jets blasted a transmission antenna for Hezbollah TV and radio on a hill overlooking Baalbek. There was no word of casualties, but the group's broadcasts stopped in that area.
In northern Israel, thousands of civilians spent last night in underground shelters as Hezbollah fired rockets across the border. A 40-year-old Israeli woman was killed and five people were wounded in the rocket attacks, the Israeli army reported.
The fighting erupted after Hezbollah captured the two Israeli soldiers in a strike that killed eight other Israeli troops. Israel blasted bridges and roads in southern Lebanon throughout yesterday.
Hezbollah leader Sheik Hassan Nasrallah offered to trade the two soldiers for Arab prisoners, and warned Israel that his guerrillas would fight if attacked.
Hezbollah has declared it has more than 10,000 rockets and has in the past struck northern Israeli communities in retaliation for attacks against Lebanese civilians.
Hezbollah's TV station reported that guerrillas fired Katyusha rockets at Israeli border town of Kiryat Shmona, targeting an airstrip in the upper Galilee panhandle. Another barrage of rockets targeted Nahariya near the coast.
A 40-year-old Israeli woman was killed when her home in the northern border town of Nahariya was struck by a rocket, Israeli medics said. The Israeli military confirmed the death.
At Nahariya Hospital, patients were moved to secure rooms on lower floors. Nahariya's Mayor Jackie Sabag said the whole town had been shut down and urged residents to stay in underground shelters.
The Israeli army said several rockets had landed more than 12 miles south of the border, showing that Hezbollah has managed to extend its missiles' range.
Early today, warplanes struck the runways of Beirut's international airport in the Lebanese capital's Hezbollah-controlled southern suburbs, Lebanese officials said.
A shell hit the eastern runway shortly after 6am (0400BST) and was followed by others, airport employees reported. An inspection found that the three runways had a total of one large crater and seven smaller holes, airport officials said.
Flights approaching the airport were diverted to Larnaca airport on the island of Cyprus. A senior airport official announced the facility had been closed and diverted scheduled flights to Cyprus.
The main terminal building of the airport, which was built in the late 1990s, remained intact.
In Cyprus, Civil Aviation Director Leonidas Leonidou said a total of five flights had been diverted to the island overnight.
It was not clear if all the shells came from Israeli aircraft or if gunboats participated in the attack on the airport, which lies close to the sea in the southern suburbs of Beirut, a stronghold of Hezbollah guerrillas.
The Israeli military confirmed it had struck Beirut airport, saying the facility is "a central hub for the transfer of weapons and supplies to the Hezbollah terrorist organisation."
It was the first time since Israel's 1982 invasion of Lebanon and occupation of Beirut that the airport in south Beirut was hit by Israel. The Israelis in 1968 sent commandos to Beirut airport, blowing up 13 passenger planes on the runway in retaliation for Arab militants firing on an Israeli airliner in Athens.
Israel said its air offensive was the fiercest since its 1982 invasion of Lebanon. The last major air, ground and sea offensive against Lebanon was in 1996 when about 150 Lebanese civilians were killed.
In its overnight attacks, Israeli aircraft and artillery targeted roads and bridges as well as Hezbollah positions and houses of guerrilla members and leaders.
A bridge on the main highway between Beirut and southern Lebanon was hit overnight by big bombs that left huge craters, blocking traffic. People who were leaving southern Lebanon had to walk around the craters near the town of Damour, about 10 miles south of Beirut.
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