As dusk fell, Israel continued to bomb the strip, firing on a metal foundry in the south.
Salam Fayyad, the Palestinian prime minister, condemned the attack and demanded an immediate cessation.
Hours after the Israeli assault, Gaza fighters fired home-made rockets into southern Israel, heeding calls by Hamas and other affiliated Palestinian groups to avenge the attacks, unprecedented in their scale.
One Israeli was killed in the rocket fire, medics said.
Taher al-Noono, a Hamas spokesman, described Israel's operation as a "massacre", adding: "However, our resolve cannot be dented and cannot be shaken. We will continue our struggle with absolute strength and steadfastness."
Islam Shahwan, a Hamas police spokesman, said a police graduation ceremony in Gaza City was struck by Israel. Among those killed was Tawfiq Jabber, the Gaza chief of police.
The Hamas-run interior ministry said all security compounds in the Strip had been destroyed.
Gaza is densely populated. Its 1.5 million residents area already experiencing shortages in medicine, power and basic supplies due to 18 months of an Israeli blockade.
Mahmoud Abbas, the Palestinian president and leader of Fatah, condemned the "aggression" in Gaza.
|Smoke billowed into the air above the Gaza Strip [AFP]
Mousa Abu Morzouz, the deputy leader of Hamas, told Al Jazeera: "Until now the aggression didn't stop ... they are targeting all the police headquarters and offices.
"We will defend our people, we will retaliate against this aggression ... our military will retaliate."
Morzouz called on the world's most powerful nations to condemn the attacks: "Nobody in this world can accept what happened and the Israeli aggression ... [we expect] the international community to stand against this and say that it is not acceptable."
Mustafa Barghouthi, the former Palestinian information minister, said: "This is not an attack on the Hamas. It is an attack on the whole population and the free will of the people of Gaza."
He accused Israel of committing "war crimes" and demanded that Abbas and his government stop all relations with Israel.
'Only just beginning'
The Israel army released a statement saying "terrorist installations" were hit and that all Israeli pilots returned unharmed.
The operation against the Hamas is "only just beginning," Avi Benayahu, an Israeli military spokesman said.
The air raids follow the decision by the Israeli security cabinet to increase reprisals for cross-border rocket attacks against Israel, and the breakdown of a six-month-old Israel-Hamas truce earlier this month.
The ceasefire expired on December 19, with Hamas arguing that Israel had violated the truce by preventing vital food and medical supplies into the Strip.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "A series of explosions were heard over Gaza City.
"From where we are, there are at least seven different clouds of smoke from the strikes. We are seeing some casualties being evacuated in cars."
Egypt has opened the Rafah crossing with the Gaza Strip to receive injured people, Egyptian officials said. Ambulances have been sent to the crossing and two Egyptian hospitals emptied to take in the wounded.
Weakened security services
Mohyeldin said that Hamas, which rule the Gaza Strip, was being held responsible by Israel for any attacks from the territory into Israel, even if they are undertaken by other Palestinian factions.
|Palestinian officials called on the international community to condemn the raids [AFP]
However, officials of the deposed government in Gaza which maintains law and order, while being Hamas member in the main, are separate from the group's military wing and other factions responsible for attacks into Israel.
"There is within Gaza a functioning ministry of interior that has security services, traffic control, emergency medical services," Mohyeldin reported.
"Those workers are seen as employees of the government in Gaza. So now that many of these installations have been targeted, it will have an immediate impact in terms of the law and order structure here in Gaza."
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said that Israel's decision to strike at this moment was down to Hamas withdrawing from the ceasefire and the intensified rocket fire coming from the Gaza Strip in recent days.
"In one day [in the past week] we saw 80 rockets ... which is a huge upsurge," she said.
Hamas won control of the Palestinian Legislative Council in elections in January 2005. The international community refused to accept a Hamas-led government, demanding that the faction recognise Israel and renounce violence. Economic sanctions by the EU and US followed.
Hamas took control of the Gaza Strip in June 2007 after bloody street battles against its rival, the Fatah movement.