Warplanes pounded Gaza for a fourth day as tanks stood by to join the "all-out" war Israel vowed would wipe out Hamas, and the Palestinian death toll rose to at least 360.
Israel made it clear on Monday the offensive was just beginning, even as UN chief Ban Ki-moon urged world leaders to work urgently to end the "unacceptable" violence.
Palestinian militants responded to Israeli air strikes with deadly rocket fire that killed three Israelis.
Defence Minister Ehud Barak, who has threatened to launch ground incursions alongside the aerial blitz, said Israel was in "an all-out war with Hamas and its proxies".
Deputy Prime Minister Haim Ramon said the offensive's goal "is to topple Hamas".
Barak said that if militant rocket attacks did not stop, "Israel will have recourse to every means and all legal actions at its disposal to see to it that the enemy halts its illegal aggression."
With Israeli tanks just metres away from Gaza, the army decreed the border area a closed military zone - a move that in the past has been followed by ground operations.
"After this operation there will not be a single Hamas building left standing in Gaza, and we plan to change the rules of the game," said armed forces deputy chief of staff Brigadier General Dan Harel, quoted by the YNet News website.
"We are hitting not only terrorists and launchers, but also the whole Hamas government and all its wings," Harel said.
At least 57 Palestinian civilians, including 21 children, have been killed in the Israeli bombardment, a UN spokesman said.
Israeli aircraft carried out dozens of air strikes under the cover of darkness early on Tuesday, targeting Hamas ministry and security buildings, Hamas sources and witnesses said.
The attacks completely destroyed the Hamas foreign and finance ministry buildings along with nearby homes, and set off fires, witnesses said.
At least 10 Palestinians were killed and 40 wounded in the latest attacks, the director of Gaza's emergency services, Moawiya Abu Hassanein said.
In all, the Israeli campaign has killed at least 360 Palestinians and wounded more than 1,690, he said.
Since the onslaught began on Saturday, Gaza militants have fired more than 250 rockets and mortar rounds into Israel, killing four people and wounding two dozen more.
On Monday, one projectile killed an Israeli Arab at a construction site in the southern city of Ashkelon some 13 kilometres north of the Gaza border.
A missile that hit a railyard in Ashdod killed a woman and wounded four more people while a rocket blast at the Nahal Oz kibbutz north of Gaza killed one person and seriously wounded another.
Three rockets also hit Ofakim in the Negev desert about 25 kilometres north of Gaza, wounding one person, Israeli emergency services said.
As the fighting continued the White House signalled strong support for Israel.
"The United States understands that Israel needs to take actions to defend itself," said spokesman Gordon Johndroe.
"They are taking the steps that they feel are necessary to deal with the terrorist threat."
At the United Nations, Ban said he was "deeply alarmed by the current escalation of violence in and around Gaza. This is unacceptable.
"Both Israel and Hamas must halt their acts of violence and... a ceasefire must be declared immediately."
He chided leaders, saying: "I think regional and international partners have not done enough. They should do more."
The UN special envoy to the Middle East on Monday also protested strongly to Israel after air strikes on Gaza hit two UN buildings and killed eight of its trainees.
US Secretary of State Condoleezza Rice was "working for a ceasefire that will be fully respected, durable and sustainable," and spoke to several world leaders including Ban, Israeli Prime Minister Ehud Olmert and his Lebanese counterpart Fuad Siniora, her spokesman said.
EU foreign ministers were set to meet in Paris on Tuesday to discuss how they can work to help ease the Gaza crisis, the French foreign ministry said.
There was also growing concern about the humanitarian situation in the aid-dependent territory of 1.5 million which Israel has virtually sealed off since Hamas seized power in June 2007.
"We ask all parties involved to allow food and medical supplies to reach the people there," the White House spokesman said.
But anger in the Muslim world is spiralling. Turkey announced it had suspended brokering preparatory peace negotiations between Syria and Israel because of the air assault as protests intensified worldwide.
Parliament in Jordan - one of two Arab states to have signed a peace treaty with Israel - demanded that the government "reconsider" relations with the Jewish state.
Western-backed Palestinian president Mahmoud Abbas, whose forces were ousted from Gaza in the Hamas takeover, implored the international community to help end "this aggression."
Hamas, which remains blacklisted by the West despite its upset victory in 2006 Palestinian parliamentary elections, lashed out at the world for not doing enough to end the blitz.
Israel is "committing a holocaust as the whole world watches and doesn't lift a finger to stop it," spokesman Fawzi Barhum told reporters.
Israel's offensive followed days of rising violence after a tenuous six-month truce in Gaza ended on December 19. It also comes ahead of early parliamentary elections in Israel called for February 10.
AFP