Israel has also closed Gaza's border with Egypt as part of a major operation in response to Palestinian shelling of Sderot - the first attack on a Jewish town in Israel proper, rather than in the Palestinian territories.
The BBC's Hilary Andersson says the mortar attack and military response are perhaps the most significant moment since the start of the Palestinian uprising last September. Each side, she says, is now clearly violating the territorial integrity of the other.
Israel says it has no intention of holding onto any Palestinian-controlled territory, but an adviser to the Israeli prime minister said the country would do what was necessary to protect Israeli lives.
A BBC correspondent who went to the Gaza Strip said there was a real sense of shock among Palestinians at the Israeli incursion.
A Palestinian cabinet minister, Hassan Asfour, accused Israel of tactics amounting to re-invasion.
"It is clear that Israel has expanded the sphere of war with the Palestinians. It has carried out a new and dangerous step by reoccupying Palestinian areas," he told Reuters news agency.
Israeli Foreign Minister Shimon Peres - the leading dove in a generally right-wing government - said the attack on Sderot "is unjustified and crosses the line. There's a limit to everything."
The Palestinian Authority denies any hand in the firing of mortars at Sderot, 5km (3 miles) from the Gaza border - the deepest shelling inside Israeli territory in the past seven months of conflict.
Hamas, the militant Islamic group, has said it carried out the attack.
Peace initiative
A new round of security talks between Israel and the Palestinians had already been cancelled before the Israeli attack on Gaza.
The violence also casts a shadow over prospects for a Jordanian-Egyptian security plan, brought to Jerusalem by Jordanian Foreign Minister Abdulilah al-Khatib.
The initiative is said to call for an end to violence by both Israelis and the Palestinians, the lifting of Israel's travel restrictions on Palestinians, a reduction of Israeli troop numbers in the Palestinian territories, and an end to the building of Jewish settlements in the West Bank and Gaza.
Mr Khatib discussed the plan with Israeli Prime Minister Ariel Sharon and Foreign Minister Peres on Monday.
Israeli officials have previously expressed reservations about the initiative.
Mr Sharon has said he will not resume political negotiations with the Palestinians until violence stops.