The Israeli government has threatened more strikes on Palestinian militant leaders, a day after it killed Sheikh Ahmed Yassin, the founder of Hamas.
Public Security Minister Tzachi Hanegbi said: "Everyone is in our sights."
Israeli security services are on high alert after Hamas vowed to avenge its leader's death.
Hamas has named Abdel Aziz al-Rantissi as its new leader in Gaza. The group will continue to have a separate leadership in the West Bank.
Hamas regards Mr Rantissi - a 56-year-old pediatrician by training - as its political leader, while Sheikh Yassin was the spiritual leader.
On Tuesday, Gaza City residents reported a series of explosions; the Israeli army later said Palestinian militants had attacked one of its armoured vehicles.
The army said troops returned fire after an anti-tank rocket was fired at the vehicle near the Jewish settlement of Netzarim.
The military said at least one mortar had been fired at the settlement.
Palestinian towns in the West Bank are sealed off and police in Jerusalem have set up checkpoints, while Israeli tanks rolled into north Gaza overnight.
Sheikh Yassin, a quadraplegic cleric who Israel says masterminded scores of suicide bombings, was targeted by helicopter gunships on Monday morning in Gaza.
His killing sparked widespread international condemnation and fury among Palestinians but the Israeli Defence Minister Shaul Mofaz said their policy of "liquidating terrorists" would continue.
Mr Mofaz, who says Hamas attacks have claimed 377 Israeli lives, described the group as a "strategic enemy of Israel" that should be destroyed.
Mr Mofaz and security chiefs decided in a five-hour meeting late on Monday to go after the entire Hamas leadership, without waiting for another
attack, security sources said.
This message was reinforced by Mr Hanegbi who told reporters on Tuesday: "Anyone who is involved in the Gaza Strip or the West Bank or anywhere else in leading a terror group knows from yesterday there is no immunity."
In the Palestinian territories, shops, schools and businesses are closed as people observe three days of mourning for Sheikh Yassin.
Posters have been put up around Gaza depicting him as a martyr.
The BBC's David Chazan in Gaza City says many people there are staying at home, steeling themselves for the possibility of more Israeli air strikes now that Israel has declared all militants on the hit list.
The few people about have an air of sullen anger, he says; and many people who do not normally support Hamas are nevertheless expressing the desire to see the militants exact a bloody revenge.
Israel has sealed off parts of the West Bank and police patrols are being stepped up in major cities, including Jerusalem, to try to stop potential bombers from reaching targets.
Israel is also bolstering security at its embassies and protection for public figures within Israel is also being stepped up, Israel Army radio reported.
A poll in Israel's top-selling Yediot Aharonot newspaper showed 60% of people backed the attack; a similar poll in the Maariv daily had 61% in favour.
But according to the Yediot poll, 81% of those questioned believed the assassination would lead to an increase in "terror attacks".
Israeli media report that Avi Dichter, the head of the country's internal security service Shin Bet, opposed the killing.
There were also dissenting voices within the Israeli cabinet.
Interior Minister Avraham Poraz said Sheikh Yassin's death could lead to more Israeli deaths in suicide attacks.
But former prime minister Ehud Barak said the Israeli government had been left with no choice but to respond to the "murderous acts on the record of this so-called spiritual leader."
"He's personally involved in directing killings of women, children and innocent citizens in the streets of Israel," Mr Barak told the BBC's Today programme.
More than 100,000 people joined Sheikh Yassin's funeral procession in Gaza City on Monday.
"The battle is open and war between us and them is open,"
said senior Hamas political leader Abdel-Aziz al-Rantissi.
Other Palestinian militant groups have also vowed revenge.