Eldad Regev (left) and Ehud Goldwasser were captured in 2006
Israel's cabinet has approved a prisoner swap with the Lebanese militant group Hezbollah.
The swap would see the return of the bodies of two Israeli soldiers captured by Hezbollah two years ago.
The Lebanese prisoners to be freed reportedly include Samir Qantar, in jail for murder since 1979.
Prime Minister Ehud Olmert said earlier that the two soldiers were dead. Their capture triggered Israel's offensive against Hezbollah in mid-2006.
The cabinet approved the German-brokered exchange by 22 votes out of 25 present at the meeting, Israeli radio reported.
Before the vote, Mr Olmert had urged his cabinet to approve the swap, even though he said the two soldiers were probably dead.
"We know what happened to them," Mr Olmert was quoted telling his cabinet by the Associated Press.
He said they had probably been killed during the raid or shortly after. Evidence from the scene of their capture indicated that at least one of them was badly wounded.
"There is no doubt that today's discussion has special weight and is exceptionally sensitive in terms of its national and moral implications," Mr Olmert said before cabinet convened.
Observers say it is the first time the Israeli government has confirmed that Ehud Goldwasser and Eldad Regev are no longer alive.
Critics have opposed swapping prisoners for the bodies of dead Israeli troops.
In exchange for the soldiers, it is reported that five Lebanese detainees are to be set free and the bodies of about 10 militants handed over.
One of these is said to be Samir Qantar, who has been in jail since 1979 for his part in a deadly guerrilla raid.
His release would be controversial in Israel because of his role in the deaths of three members of one family, says the BBC's Wyre Davies in Jerusalem.
Qantar is serving several life sentences for murder after attacking a civilian apartment block in Nahariya in 1979. A policeman, another man and his four-year-old daughter were killed. A baby girl was accidentally smothered by her mother as she hid in a cupboard.
Hezbollah has given no public indication that the two Israeli soldiers are still alive.
Israel fought a war with Hezbollah in 2006
The Red Cross has never been allowed to see them and many in Israel assume they are dead.
Israel and Hezbollah fought a 34-day war after the soldiers were seized by Hezbollah in a cross-border raid into Israel in July 2006.
Germany has been trying to broker a prisoner exchange since the war ended.
On 1 June, Hezbollah handed over the remains of five Israeli soldiers killed in the war.
The remains were delivered after Israel released a Lebanese-born man who had served six years in prison for spying for Hezbollah.
Another Israeli soldier, Gilad Shalit, remains a prisoner of the Palestinian Islamist movement Hamas.
He was seized in a raid on an Israeli army position inside Israel. Hamas has said it would consider releasing him as part of a prisoner exchange.