Israel bombarded bridges and a power station from the air to pressure militants to release a captured soldier. No casualties were reported.
It was Israel's first ground offensive since it pulled all of its soldiers and settlers out of Gaza over the summer, and Palestinians, holed up at home, were bracing for a major strike.
Israeli prime minister Ehud Olmert said Israel wouldn't balk at "extreme action" to bring the soldier home, but had no intention of reoccupying Gaza.
Palestinian president Mahmoud Abbas deplored the incursion as a "crime against humanity," and a leading Hamas politician issued a call to arms against the Israeli troops.
Overnight, Israeli tanks and soldiers began taking up positions east of the Gaza town of Rafah under cover of tank shells, witnesses and Palestinian security officials said.
Israeli warplanes fired at least nine missiles at Gaza's only power station, cutting electricity to 65 per cent of the Gaza Strip, engineers at the station said. The station's three functioning turbines and a petrol reservoir were engulfed in flames, raising the spectre of a humanitarian crisis in Gaza, because water pumps in the strip are powered by electricity.
The Israeli military said in a statement that three bridges were attacked "to impair the ability of the terrorists to transfer the kidnapped soldier," Cpl. Gilad Shalit, 19.
Knocking down the bridges cut Gaza in two, Palestinian security officials said.
Witnesses reported heavy artillery shelling near the long-closed Gaza airport into an village east of Rafah, and warplanes also flew low over Gaza City, rocking the city with sonic booms and shattering windows.
Troops in Israel backed up the assault, firing artillery into Gaza.
"We won't hesitate to carry out extreme action to bring Gilad back to his family," Olmert said. "All the military activity that started overnight will continue in the coming days."
"We do not intend to reoccupy Gaza. We do not intend to stay there. We have one objective, and that is to bring Gilad home," he added.
Olmert repeated that Israel would not negotiate Shalit's release with militant groups.
Shalit was taken captive on Sunday during a Palestinian attack on a military post in southern Israel.
Israeli Justice Minister Haim Ramon said Israel would try to assassinate Khaled Mashaal, a Syrian-based Hamas leader who Israel thinks ordered the soldier's capture.
"He is definitely in our sights ... he is a target," Ramon told Army Radio. "Khaled Mashaal, as someone who is overseeing, actually commanding the terror acts, is definitely a target."
Hamas militants and allied factions claimed responsibility for the attack on a southern military post on Sunday in which Shalit was captured and two soldiers were killed. The Palestinian government has called for the soldier's release, but Israel thinks the Syria-based leaders called the shots.
Abbas deplored the Israeli invasion in a statement.
"The president considers the aggression that targeted the civilian infrastructures to be collective punishment and a crime against humanity," the statement said. Abbas, it added, urged the US and international Mideast negotiators to intervene to halt the operation.
Normally bustling streets in southern Gaza were eerily deserted mid-morning, with people holed up inside their homes. A few children from nearby Bedouin encampments played in the streets, and two women in a donkey cart drove near the airport in Rafah.
The Rafah crossing between Gaza and Egypt - Gaza's main link to the outside world - has been closed since the attack on Sunday in which the Israeli soldier was taken captive. Usually, there is some activity in the area, even when the passage is closed, but today, it was empty.
Masked militants from various armed factions took up defensive positions around Gaza City in the northern part of the strip. Militants said they fired a rocket early Wednesday at the Israeli village of Nahal Oz, the Israeli forces' staging area, and at other Israeli targets.
Capt. Jacob Dallal, a military spokesman, said the army was prepared for a long operation, if necessary.
"We have a vast variety of military options available to us and everything is on the table," he said. At the same time, Israel is keeping diplomatic channels open during the Gaza operation with the hope that contacts could win the soldier's release, Dallal said.
The militants who seized Shalit have demanded the release of hundreds of Palestinian women and children held in Israeli jails in exchange for information about the captured soldier.
Trying to defuse building tensions, negotiators from the ruling Hamas movement said they had accepted a document implicitly recognising Israel. But two Syrian-based Hamas leaders, who hold great weight within the movement, denied a final deal had been reached.
Shalit's abduction on Sunday by Hamas' military wing and two other Hamas-linked groups has threatened to turn already devastated relations between Israel and the Hamas-led government into an all-out war.
Hamas took over the Palestinian Authority after winning parliamentary elections in January, and has been under international pressure to renounce violence and recognise Israel.
Complicating matters was a new claim by the Hamas-linked Popular Resistance Committees, one of the three groups that carried out Sunday's assault, that it had also kidnapped a Jewish settler in the West Bank.
Police spokesman Micky Rosenfeld said the report was being taken "very seriously," and military officials said there was "rising fears" the claim was true.
After Israel launched its Gaza assault, the PRC threatened to kill its hostage.
Israeli aircraft struck a training camp of the Hamas militant group in the Gaza Strip town of Rafah, witnesses said. The army had no immediate comment. Two missiles fell about 200 metres apart, one in an empty training camp for Hamas, witnesses said. The other rocket hit an empty field nearby, and witnesses said they saw militants running away from the missile. Ambulances had no immediate reports of injuries.
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