Israeli F-16 bombers have pounded key targets across the Gaza Strip, killing at least 195 people, medics say.
Gaza officials and the Hamas militant group said more than 300 others were hurt as missiles hit security compounds and militant bases.
The strikes, the most intense Israeli attacks on Gaza for decades, come days after a truce with Hamas expired.
Israel said it was responding to an escalation in rocket attacks from Gaza and would bomb "as long as necessary".
Israeli Defence Minister Ehud Barak said "it won't be easy and it won't be short".
"There is a time for calm and a time for fighting, and now the time has come to fight," he said, quoted by Reuters.
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Palestinian militants frequently fire rockets against Israeli towns from inside the Gaza Strip; large numbers of rocket and mortar shells have been fired at Israel in recent days.
In a statement, Israel's military said it targeted "Hamas terror operatives" as well as training camps and weapons storage warehouses.
A Hamas police spokesman, Islam Shahwan, said one of the raids targeted a police compound in Gaza City where a graduation ceremony for new personnel was taking place.
At least a dozen bodies of men in black uniforms were photographed at the Hamas police headquarters in Gaza City.
Israel's Foreign Minister Tzipi Livni defended the air raids, saying Israel had "no choice". "We're doing what we need to do to defend our citizens," she said in a television broadcast.
Israel hit targets across Gaza, striking in the territory's main population centres, including Gaza City in the north and the southern towns of Khan Younis and Rafah.
In the West Bank, Palestinian Authority President Mahmoud Abbas - whose Fatah faction was ousted from Gaza by Hamas in 2007 - condemned the attacks and called for restraint.
But Hamas quickly vowed to carry out revenge attacks on Israel in response to the air strikes, firing Qassam rockets into Israeli territory as an immediate reply.
At least one Israeli was killed by a rocket strike in the town of Netivot, doctors said.
"Hamas will continue the resistance until the last drop of blood," spokesman Fawzi Barhoum was reported as saying.
Israel also stood firm, saying operations "will continue, will be expanded, and will deepen if necessary".
It is the worst attack in Gaza since 1967 in terms of the number of Palestinian casualties, a senior analyst told the BBC in Jerusalem.
The air strikes come amid rumours that an Israeli ground operation is imminent.
Calls for ceasefire
International reaction was swift and expressed concern, with many world leaders calling for calm and an immediate ceasefire.
Palestinians flee the scene of an air strike in Rafah
Civilians were caught up in the air strikes in heavily-populated Gaza
A White House spokesman said the United States "urges Israel to avoid civilian casualties as it targets Hamas in Gaza".
"Hamas' continued rocket attacks into Israel must cease if the violence is to stop," the spokesman, Gordon Johndroe, added.
The UK Foreign Office said: "We urge maximum restraint to avoid further civilian casualties."
The French presidency of the EU meanwhile called for an immediate halt to the shooting by both sides.
At least 30 missiles were fired by F-16 fighter bombers. Israel's Haaretz newspaper reported that some 60 warplanes took part in the first wave of air strikes.
Hamas said all of its security compounds in Gaza were destroyed by the air strikes, which Israel said hit some 40 targets across the territory.
Mosques issued urgent appeals for people to donate blood and Hamas sources told the BBC's Rushdi Abou Alouf in Gaza that hospitals were soon full.
Egypt opened its border crossing to the Gaza Strip at Rafah to absorb and treat some of those injured in the south of the territory.
Most of the dead and injured were said to be in Gaza City, where Hamas's main security compound was destroyed. The head of Gaza's police forces, Tawfik Jaber, was reportedly among those killed.
A resident describes the attacks in Gaza
Images from the targeted areas showed dead and injured Palestinians, burning and destroyed buildings, and scenes of panic and chaos on Gaza's crowded streets.
Residents spoke of children heading to and from school at the time of the attacks, and there were fears of civilian casualties.
Reuters news agency said at least 20 people were thought to have died in Khan Younis.
Israeli security officials have been briefing about the possibility of a new offensive into Gaza for some days now, says the BBC's Paul Wood, in Jerusalem.
But most reports centred on the possibility of a ground offensive, and Prime Minister Ehud Olmert was not expected to authorise any operation until Sunday at the earliest.
Although a six-month truce between Hamas and Israel was agreed earlier this year, it was regularly under strain and was allowed to lapse when it expired this month.
Hamas blamed Israel for the end of the ceasefire, saying it had not respected its terms, including the lifting of the blockade under which little more than humanitarian aid has been allowed into Gaza.
Israel said it initially began a staged easing of the blockade, but this was halted when Hamas failed to fulfil what Israel says were agreed conditions, including ending all rocket fire and halting weapons smuggling.
Israel says the blockade - in place since Hamas took control of Gaza in June 2007 - is needed to isolate Hamas and stop it and other militants from firing rockets across the border at Israeli towns.
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