Israeli troops have dug into positions in south Gaza, having crossed the border overnight following air strikes on three bridges and a power station.
Palestinian ruling party Hamas has condemned attacks on the infrastructure and called for a prisoner exchange - which Israel has rejected.
Militants say they have abducted two more Israelis - both civilians.
Sporadic strikes
On Wednesday evening Israeli tanks resumed artillery fire over the border into Gaza, as troops strengthened positions around Gaza's disused airport.
Israel said it had targeted a weapons factory in the southern town of Khan Younis in an air strike on Wednesday evening.
The attack followed sporadic air strikes throughout the day. Israel said it was firing into open fields.
Targets included a rocket-making factory and a Hamas training camp, witnesses said.
There were no immediate reports of casualties.
The overnight raid destroyed Gaza's main power station and nervous civilians in northern Gaza stockpiled batteries and candles, as well as food and water.
Streets were deserted in the south as families hunkered down in the homes.
'Right to defend'
Israeli Prime Minister Ehud Olmert said Israel would not hesitate to "carry out extreme action" to free the captured soldier - 19-year-old Corporal Gilad Shalit - but said Israel did not want to re-take control of Gaza.
"We are living, but we feel as if we are dead"
Palestinian Authority President Mahmoud Abbas described the incursion as a "crime against humanity" and Prime Minister Ismail Haniya of Hamas warned Israel to "stop the military escalation".
The White House said Israel had "the right to defend itself" but should ensure civilians were not harmed.
Israel also blamed Syria-based Hamas leaders for the abduction of Corporal Shalit, and threatened to target them.
Israeli warplanes flew warning sorties over the summer residence of Syrian President Bashar-al Assad early on Wednesday morning.
Syria said it had responded with anti-aircraft fire.
Missing civilians
Cpl Shalit was taken prisoner in a raid claimed by three different organisations - including the armed wing of governing party Hamas - on an Israeli guard post near Gaza on Sunday.
Israel has refused a demand from the groups that Palestinian women and children held in Israeli jails to be freed in exchange for information about the soldier.
CAPTURED ISRAELI SOLDIER
Militants also say they have abducted two Israeli civilians.
On Wednesday, members of the Popular Resistance Committees in the West Bank showed what appeared to be a photocopy of the ID card of a settler they said they had abducted.
A spokesman said the group would kill 18-year-old Eliyahu Asheri, who has been missing since Monday, if Israel continued military action.
Hamas political leaders have denied they know of Cpl Shalit's whereabouts and have urged his captors not to mistreat him.
Israel last year pulled soldiers and thousands of settlers out of Gaza, which it had first occupied after the 1967 war.
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