Speaking after the start of the Gaza offensive, Ehud Olmert said on Wednesday that Israel would not shy away from "extreme action" to bring the soldier home.
"We won't hestitate to carry out extreme action to bring Gilad back to his family," he said, referring to Corporal Gilad Shalit.
"All the military activity that started overnight will continue in the coming days."
Shalit was captured by Palestinian fighters on Sunday in an attack on an Israeli guard post near Gaza which left two more Israeli soldiers dead and two fighters dead.
In response, Israeli troops and tanks moved into southern Gaza after overnight airstrikes that destroyed three bridges and a power station, leaving much of the strip, where 1.4 million Palestinians live, without electricity.
Engineers said repairs could take six months.
An Israeli aircraft also carried out an air strike against a training ground used by Hamas fighters in southern Gaza on Wednesday, Palestinian sources said.
A Palestinian security source said an aircraft fired at least one missile at the camp used by the armed wing of Hamas.
The Israeli military confirmed only that it had carried out two aerial attacks on open fields in the southern part of the Palestinian territory.
Olmert said his country had no intention of re-occupying the territory, which Israel withdrew from in August 2005.
Israeli warplanes fired at least
one missile at a Hamas camp
"We have one objective, and that is to bring Gilad home," he added, reiterating that Israel would not negotiate with Palestinian groups for the soldier's release.
Mahmoud Abbas, the Palestinian president, condemned Israel's offensive, calling it a "crime against humanity" and collective punishment for the Palestiniain people.
He also called in a statement for international action to halt the incursion.
Musheer al-Masri, a Hamas spokesman, has condemned Israel's destruction of Palestinian infrastructure facilities.
"The whole world now witnesses war crimes and state terrorism which Israel is practising against the Palestinian people," al-Masri said.
"Israel's demolition of the Palestinian infrastructure; destroying bridges linking Gaza Strip areas and the only electricity station in the strip, represents nothing but a Zionist failure in relation to the Palestinian resistance.
"It also means that the objective of this Zionist enemy is to destroy the rest of the Palestinians' vital facilities and economic resources.
Masri (L): Israel aims to destroy
vital Palestinian facilities
"We will not retract, we will go forward."
Speaking on the Hamas radio station, Nizar Rayan, a senior political figure of the Islamist group, urged Palestinian fighters to arm themselves and fight the Israeli troops in "the battle of liberating the prisoners".
Fighters holding the Israeli soldier hostage have demanded the release of hundreds of Palestinian women and children from Israeli jails.
The Bush administration has declined to condemn Israel for knocking out electricity and water supplies for most residents of the Gaza Strip.
White House press secretary Tony Snow on Wednesday urged Hamas to release the soldier and urged Israel not to harm innocent civilians and "avoid the unnecessary destruction of property and infrastructure" as it tries to get him back.
"The hostage-taking and the attacks by Hamas last weekend have precipitated the current events in Gaza," he said.
"Israel has the right to defend itself and the lives of its citizens. ... Let's just point out, once again, you have the Israeli forces trying to reclaim somebody who was kidnapped and is being held hostage in Gaza. And they are doing what they can to return him."
Snow would not comment on any of the specific actions taken by Israel.
Meanwhile, a senior Israeli cabinet minister has said the Syria-based Hamas leader, Khalid Mishaal, is a target for assassination after Shalit's kidnapping.
"He is definitely in our sights," Haim Ramon, the Israeli justice minister, told Israeli army radio on Wednesday.
"Mishaal, as someone who is overseeing, actually commanding the terror acts, is definitely a target."
Israel, which has tried to assassinate Mishaal before, holds the Hamas leader responsible for Sunday's kidnapping.