"You wanted an open war. You will get an open war," Nasrallah said in a telephone message broadcast live on Hezbollah television after the attack.
He said an Israeli navy ship was ablaze off the coast of Beirut.
The Israeli military confirmed that the vessel had been badly damaged and that four Israeli troops were missing at sea.
Israeli media reported that the ship was hit by an unmanned airborne drone packed with explosives.
"You wanted an open war. You will get an open war"
Sayyed Hassan Nasrallah, the Hezbollah chief
The army had said earlier that the attack from the shore had caused only light damage.
"Look at it burn," Nasrallah declared in his address. "It will sink and along with it dozens of Zionist soldiers."
Celebratory gunfire erupted in the Lebanese capital and drivers honked their horns after Nasrallah's speech.
The Syrian- and Iranian-backed Islamist group, which wants to trade its captives for prisoners held in Israel, fired more rockets across the frontier, killing an Israeli woman and child.
Israeli air strikes destroyed Nasrallah's apartment building and a main Hezbollah office in southern Beirut. Hezbollah said Nasrallah and his family and bodyguards were safe.
An Israeli army spokeswoman would not say if the intention had been to kill Nasrallah. "We targeted the headquarters of Hezbollah in southern Beirut. We attacked two structures that are used by the leadership of Hezbollah," she said.
Syria backs Hezbollah
Meanwhile, Syria has said it will support its allies Hezbollah and Lebanon against Israel's attacks on the country.
"The Syrian people are ready to extend full support to the Lebanese people and their heroic resistance to remain steadfast and confront the barbaric Israeli aggression and its crimes," a communique from the ruling Baath party's national command said on Friday.
The national command is the highest echelon of the Baath Party, which has ruled Syria since 1963.
"The meeting discussed the dangerous developments that resulted from escalation of the Israeli aggression in the occupied Palestinian land and Lebanon, and the barbaric war and state terrorism practised by Israel," the communique said.
Israel also attacked many Lebanese civilian installations on the third day of its campaign to force the release of the two Israeli soldiers and halt cross-border rocket strikes.
Israel has also attacked many
The assault has drawn mounting international criticism, but the White House said President Bush would not press Israel to halt its military operation.
Asked whether Bush had agreed to a request from Fouad Siniora, the Lebanese prime minister, to rein in Israel, Tony Snow, the White House spokesman, said that the president "is not going to make military decisions for Israel."
The Lebanon violence is the fiercest since 1996 when Israel launched a 17-day blitz on Hezbollah strongholds in the south, four years before its troops pulled out of Lebanon.
Israeli aircraft rocketed runways at Beirut's already closed international airport and bombed a flyover just to the south.
Israeli warplanes blasted the main Beirut-Damascus highway overnight, tightening an air, sea and land blockade of Lebanon, and bombed targets in Beirut's teeming Shi'ite Muslim suburbs, killing three people and wounding 40, security sources said.
Air strikes in south Lebanon killed five more people.
Their deaths brought to 66 the number of people, almost all civilians, killed in Lebanon in the past three days.
Hezbollah rocket attacks on northern Israel have now killed four Israelis and wounded more than 150.
The Israeli prime minister's office said such salvos "cannot and will not be allowed to continue".
Snow told reporters that Bush had spoken to Lebanon's prime minister among other Middle East leaders.
He said that Bush believed the Israelis had the right to protect themselves, but should avoid civilian casualties and damage.
Israel holds Lebanon responsible for the actions of Hezbollah, a political-military faction which has members in parliament and in Siniora's mainly anti-Syrian cabinet.
Israel's Gaza offnsive launched on
June 28 has killed 80 Palestinians
The fragile Beirut government, too divided to disarm Hezbollah or extend its own control to the border, urged the UN Security Council to tell Israel to halt its onslaught.
It asked the Council to impose a ceasefire, but Israel said it was trying to free its neighbour from terrorist occupation and insisted the Beirut government secretly backed its actions.
Strong criticism of Israel came from France and the Vatican, as well as Egypt, Jordan and other countries.
The violence in Lebanon coincided with an Israeli incursion into the Gaza Strip launched last month to try to retrieve another captured soldier and halt Palestinian rocket fire.
Israel bombed offices of Hamas lawmakers, destroyed a bridge and fired a tank shell that killed a Palestinian on Friday.
Israeli forces withdrew overnight from central Gaza after two days of fighting, but did not rule out going back in.
Meanwhile Palestinian gunmen blew a huge hole in the border wall between Gaza and Egypt, allowing hundreds of Gazans who had been stranded on the closed border for two weeks to enter the Strip.
Since the Gaza offensive was launched on June 28, Israel has killed more than 80 Palestinians, a majority of them militants.