The Israeli government agreed Sunday to free a Lebanese gunman convicted in one of the grisliest attacks in the country's history in exchange for the bodies of two Israeli soldiers killed by Hezbollah guerrillas.

The German-mediated deal was a rare political victory for embattled Prime Minister Ehud Olmert and closed a chapter from Israel's inconclusive war against the Lebanese militant group two years ago.

But critics warned that the deal's heavy price for Israel could offer militant groups an even greater incentive to kill captive soldiers. In Lebanon Sunday, Hezbollah declared victory and planned celebrations.

Israel's Cabinet voted 22-3 to OK the deal to return the bodies of Ehud Goldwasser and Eldad Regev, captured by Hezbollah in a July 2006 cross-border raid that sparked a vicious monthlong war.

Before a six-hour Cabinet debate, Olmert announced for the first time that the soldiers were dead. He nevertheless pushed for the deal to be approved, citing the country's deep moral commitment to its dead and captive soldiers.

"Since we were children, we have been taught that we don't leave wounded in the field and we don't leave soldiers in captivity without doing all we can to free them," he said.

Israel will also receive the remaining body parts of its soldiers from the Lebanon war and a thorough Hezbollah report about Ron Arad, a missing Israeli airman whose plane crashed in Lebanon in 1986.

The most difficult part for Israel was the release of Samir Kantar. He is serving multiple life sentences for infiltrating northern Israel in 1979 and killing three Israelis — a 28-year-old man, his 4-year-old daughter and an Israeli police officer.

Witnesses said Kantar smashed the little girl's head against a rock and crushed her skull with a rifle butt. The attack has been etched in the Israeli psyche as one of the cruelest in the nation's history. Kantar denied killing the girl or smashing her skull.

Her mother, while trying to silence the cries of her other daughter as Kantar and three others rampaged through the apartment, accidentally smothered the 2-year-old.

On Sunday, the mother, Smadar Haran Kaiser, said she was devastated by the 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."

Israel also agreed to release four other Lebanese prisoners, dozens of bodies and an undisclosed number of Palestinian prisoners.

Finance Minister Ronnie Bar-On, who voted against the deal, told The Associated Press that he objected to the deal because "it included releasing Palestinian prisoners."

Dovish lawmaker Yossi Beilin told Channel 10 TV he would have backed the deal if the soldiers were still alive.

"There is tremendous difference in my view between saving someone's life and receiving coffins," he said. "I pray that we didn't give these people ideas that they can carry out more kidnappings and then ask for whatever they want."

Israel was also negotiating a trade with Palestinian Hamas militants for the release of an Israeli soldier captured in a June 2006 cross-border raid from the Gaza Strip.

Unlike his comrades in Lebanon, the soldier, Sgt. Gilad Schalit, 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 either.

In Beirut, Hezbollah said the Israeli approval of the deal 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.

In the southern city of Sidon, members of the Popular Democratic Party were decorating the central Martyrs Square with pictures of Kantar and hanging banners such as "Freedom to the hero, prisoner Samir Kantar" and "freedom comes with blood not tears."

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, Olmert said for the first time that Israel has concluded the two soldiers were 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, praised Olmert for pushing for the trade, while still trying to come to terms with his 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."

Israeli officials said the deal could take place as early as next week. The trade will likely take place in Germany.

Ofer Regev, brother of kidnapped soldier Eldad Regev, said he hadn't given up hope yet.

"Until we see otherwise, we will continue hoping for a miracle to happen to us," he said.

ARON HELLER