Israel's cabinet approved a deal Sunday that would see it trade a Lebanese prisoner for the bodies of two soldiers captured by Hezbollah in July 2006.

In conjunction with the controversial deal, Israeli Prime Minister Ehud Olmert said officially for the first time that the two soldiers were dead.

"We know what happened to them," Olmert said in a statement released by his office. "As far as we know, the soldiers (Eldad) Regev and (Ehud) Goldwasser are not alive."

If Hezbollah also approves the deal, Samir Kantar, who has been in prison in connection with a 1979 attack on an Israeli town, would be returned for the bodies of the two soldiers.

Kantar was convicted of shooting and killing an Israeli man. Witnesses said Kantar -- 16 at the time -- also killed the man's four-year-old daughter by smashing her head against a rock with his rifle butt.

The man's wife -- who was hiding during the attack -- also accidentaly killed another daughter during the attack by smothering the girl. She was trying to keep the two-year-old quiet so Kantar and others involved in the attack would not find them.

The possibility of a swap has been controversial. Mossad and other security agencies have opposed the deal, officials said. Critics have also said the deal would give Israel's enemies another reason to capture their soldiers.

But the soldiers' families had mounted a campaign pushing for the deal.

Goldwasser's father, Shlomo, said he wants more proof before he believes his son is dead.

"There have been assessments for a long time," he said. "But none of this matters because it is not fact. ... They were alive when they (were) kidnapped and no one has provided us with evidence to the contrary."

Israel had claimed the capture of the soldiers during a cross-border raid by militants led to their 34-day war with Lebanon in 2006.

With files from The Associated Press