Israel's Cabinet voted overwhelmingly on Sunday in favor of an emotionally charged deal to swap a Lebanese convicted in a brutal 1979 attack for the bodies of two Israeli soldiers declared earlier in the day to be dead.

The deal with the Lebanese Hezbollah militant group has sparked a fierce debate over whether Israel would be giving up too much — or carrying out its highest commitment to its soldiers to do everything possible to bring them home if they fell into enemy hands.

Hezbollah militants captured Ehud Goldwasser and Eldad Regev in a July 2006 cross-border raid that sparked a vicious, monthlong war.

In return for their bodies, the Cabinet agreed to release Samir Kantar, a Lebanese guerrilla imprisoned for nearly 30 years for an attack etched in the Israeli psyche as one of the cruelest in the nation's history.

Hezbollah had offered no sign that Goldwasser and Regev were alive and the Red Cross was never allowed to see them. Ahead of the vote, Prime Minister Ehud Olmert said for the first time that Israel has concluded the two soldiers were dead — killed during the raid or shortly after.

"We know what happened to them," Olmert told the Cabinet, according to comments released by his office. "As far as we know, the soldiers Regev and Goldwasser are not alive."

Goldwasser's wife, Karnit, who has traveled the world to press leaders to push for her husband's release, said she was still trying to come to terms with the prime minister's declaration.

"My heart aches. It is very difficult for me. I am very tired, drained inside," she told reporters. "All I want to do is to digest things, try to understand what happened ... to rest a bit ... to have my pain."

In exchange for the soldiers' bodies, the Cabinet was asked to agree to give up Kantar, who is serving multiple life terms in a 1979 infiltration attack on a northern Israeli town. Witnesses said Kantar — then 16 — shot Danny Haran in front of his 4-year-old daughter, then smashed her skull against a rock with his rifle butt, killing her, too.

During the attack, Danny Haran's wife accidentally smothered their 2-year-old daughter in a frantic attempt to keep her quiet as they hid in the crawl space of their apartment. Two Israeli policemen also were killed. Kantar denies killing the 4-year-old.

In Beirut, Hezbollah said the Israeli decision reflected the guerrilla group's strength.

"What happened in the prisoners issue is a proof that the word of the resistance is the most faithful, strongest and supreme," the group's Al-Manar TV quoted Hezbollah's Executive Council chief Hashem Safieddine as saying.

The Cabinet debated the deal for nearly six hours before approving the vote 22 to 3.

In addition to the bodies, Israel will receive a report on a missing Israeli airman whose plane crashed in Lebanon in 1986, and body parts of other Israeli soldiers.

In addition to Kantar, Lebanon will receive four imprisoned Hezbollah fighters, a dozen bodies, most of them Hezbollah militants, and an unspecified number of Palestinian prisoners. Hezbollah had demanded the release of hundreds of Palestinian prisoners.

Israel's military chief of staff, the head of the Mossad intelligence agency, the commander of the Shin Bet security service and other defense officials briefed ministers before the vote. The Mossad and Shin Bet chiefs opposed the deal, while military chief Lt. Gen. Gabi Ashkenazi supported it, officials said.

Critics have argued that swapping bodies for Kantar would offer militant groups an even greater incentive to capture soldiers and less of a reason to keep captives alive.

In addition to the two captured soldiers held in Lebanon, Israel is trying to win back a third soldier captured by Palestinian militants in a June 2006 cross-border raid from the Gaza Strip. Unlike his comrades in Lebanon, the soldier has sent letters and an audio tape to his parents and is believed to be alive, though he has not been seen since his capture and the Red Cross has not been permitted to visit him.

The proposed deal with Hezbollah would require the approval of the militant group's secretive, decision-making Shura Council. Germany has been trying to mediate a prisoner exchange since Israel's war with Lebanon ended in August 2006.

Israeli media said the soldiers' bodies would be sent to Germany and identified by Israel before Kantar is released. The identification process and swap are expected to take 10 to 14 days, Israeli media reported.

The debate over whether to trade an infamous attacker for two soldiers believed to be dead taps into a military ethos that runs deep within Israeli society, where most young men and many young women perform compulsory service. Soldiers go out to battle with the understanding they won't be left behind in the field.

The controversy also has weighed the immediacy of the Regev and Goldwasser families' anguish against the pain suffered by a family attacked nearly 30 years ago.

The woman whose family Kantar killed, Smadar Haran Kaiser, said she was devastated by Sunday's decision, but understood it.

"The despicable murderer Kantar was never my own personal prisoner, but the state's prisoner," she told a news conference. "Even if my soul should be torn, and it is torn, my heart is whole."

In the past, she had opposed Kantar's release.

"There is no doubt that today's discussion has special weight and is exceptionally sensitive in terms of its national and moral implications," Olmert said at the start of the Cabinet meeting.

Israeli newspapers splashed pictures of the soldiers, their families and military comrades on their front pages. "Bring them home," ran the headline of the Yediot Ahronot mass-circulation daily. "Look us in our teary eyes," ran the headline in Maariv, under a picture of Goldwasser's parents and Regev's father.

The soldiers' families had mounted a concerted public campaign to get the government to vote for the swap. Family and friends demonstrated outside Olmert's office while the ministers deliberated.

Some politicians were afraid the emotional appeals of the soldiers' families could lead the government to bend sacred principles.

"If they are dead, I certainly oppose this deal," dovish lawmaker Yossi Beilin told Israel Radio before the Cabinet meeting began. "The principle must be releasing live prisoners for live hostages, and releasing bodies in return for the fallen."

When Israel has agreed to prisoner swaps in the past, the terms have been dramatically disproportionate. In one hotly contested exchange, Israel in 1985 released 1,150 Arab prisoners, almost all of them Palestinians, in exchange for three soldiers captured by Lebanese guerrillas in 1982. The debate over that deal flared when some of the freed prisoners played key roles in a Palestinian uprising against Israel that began in 1987.

Militants have tried for years to get Kantar released. But Israel has held on to him for nearly three decades, hoping to use him as a bargaining chip to wring information from Hezbollah about the fate of the missing Israeli airman, Ron Arad.

Recently, Israeli leaders concluded Hezbollah has no new information about Arad. His family — which had been told by a previous government that Kantar would not be released without more information about Arad's whereabouts — shunned an invitation to meet with Olmert to discuss the prisoner swap.

But in the end, Hezbollah agreed to turn over additional information about Arad.