The 20-year-old soldier, who also holds French nationality, was snatched in a brazen raid on an army post on the Gaza Strip border at dawn on Sunday in which two other Israeli servicemen and two Palestinian fighters were killed.
Israel has been massing troops on the border to prepare for any retaliatory operations after Sunday's assault by gunmen who tunnelled their way under the border and attacked the post with rockets and bombs.
It was the deadliest militant assault in the area since last summer when Israel pulled out of the Gaza Strip, which has since become plagued by lawlessness and deadly feuding between rival political factions.
"Yesterday I instructed the heads of the army to deploy our forces in order to be ready to prepare for a prolonged and extensive military operation in order to strike the terror organisations and commanders," Olmert said.
"We will reach everyone, anywhere and they know. There will be no immunity for anyone," he added in a speech in Jerusalem.
"We consider the Palestinian Authority on all its senior levels, from the chairperson down to the prime minister, as the element responsible for this operation (Sunday's attack) and everything that it implies."
Palestinian president Mahmud Abbas has condemned the attack while the Hamas-led Palestinian government, boycotted by both Israel and the West as a terrorist organisation, has demanded the immediate release of the soldier.
Hamas' armed wing was among three militant groups which claimed Sunday's assault to avenge the deaths of 22 Palestinian civilians killed in one alleged Israeli shelling and a series of botched air strikes.
A representative of the Popular Resistance Committees, which claimed the attack together with the Hamas wing and the previously unheard of Army of Islam, said in a telephone call to AFP that it was holding the soldier.
"He is alive and in good health," the representative of the group said on condition of anonymity. "He is not seriously injured."
He gave no indications as to the whereabouts of the missing soldier, Gilad Shalit, whose bloodstained flak jacket was found near the scene of the attack, according to the Israeli army.
Foreign Minister Tzipi Livni, Olmert's official number two, said it was Israel's "natural and legitimate right" to use military force in an effort to retrieve the missing soldier.
Urging the international community to "unequivocally condemn" the abduction, Livni told foreign ambassadors that if mediation efforts fail, Israel would be forced to use military might to bring about the soldier's release.
"It's the natural and legitimate right of every state for self defence," a foreign ministry spokesperson quoted her as saying.
A high-ranking security official also said Israel would work to topple the Hamas-led government ? boycotted financially and politically by the West since taking office in March ? unless the soldier is released alive.
"We will make sure that the Hamas government ceases to operate if the kidnapped soldier is not returned to us alive," the source told AFP.
Yuval Diskin, the head of Israel's Shin Beth domestic security agency, made the threat to Palestinian president Mahmud Abbas on Sunday, the source said.
Israel, which refuses to have any dealings with the terror-blacklisted Hamas, is exerting huge pressure on Abbas to resolve the crisis, blaming both the moderate president and the Hamas-led government for the attack.
Faced with the largest assault in the volatile border area since Israel withdrew all troops and settlers from Gaza last September following a 38-year occupation, Israel has vowed to avenge any harm done to the soldier.
Outside the Kerem Shalom gate into Gaza, the army was busy amassing tanks, ground troops and artillery, waiting for the green light from political leaders for any possible attack, a security source told AFP.
An Egyptian security delegation which rushed to Gaza has established contact with the abductors through a third party, Israeli radio said.
France also said it was "in contact with all the concerned parties to find a solution to this situation."
The parents of Shilat appealed in a letter for the safe release of their son, while Israel's army chief Dan Halutz ordered a full military inquiry into Sunday's attack.
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