Israel had warned of a ground invasion of Gaza even before the latest rocket attacks, which were apparently in retaliation against a series of Israeli air strikes that began on Wednesday (local time).
The Palestinian toll has now risen to 15, including the commander of the military wing of Hamas, Ahmed al-Jabari.
Jabari had long topped Israel's most wanted list, and had been accused of masterminding a string of deadly attacks, including the capture of Israeli soldier Gilad Shalit in 2006.
His car became a flaming wreck as it was struck by an Israeli missile as he travelled through Gaza City.
It was part of what Israeli defence spokeswoman Avital Leibovitch called "Operation Pillar of Defence".
"The goal of this operation is to protect the people of Israel, who have been under constant rocket attack," she said.
The Israeli Air Force pounded the Gaza Strip with more than 20 air strikes, hitting what it says were rocket storerooms and sending civilians running for cover.
Hamas has fired dozens of rockets into southern Israel, killing three civilians in an apartment block in the town of Kiryat Malachi. Three Hamas rockets also reportedly hit the city of Dimona, next to Israel's nuclear facilities.
ABC Middle East correspondent Matt Brown is near a military checkpoint just on the north of the Gaza Strip.
Israel has promised further action, including a possible ground offensive.
"Today we've sent a clear message to Hamas and to other terrorist organisations," prime minister Benjamin Netanyahu said.
"And if there is a need, the Israeli Defence Forces are prepared to widen the operation. We'll continue to do everything to defend our citizens."
Palestinians are calling for retaliation.
"Our Zionist enemy will, God willing, pay a price for this cowardly assassination," Hamas official Khalil Al Haya said.
Israelis are bracing themselves for a long stay in protective shelters as their army warns Hamas that all its men are in their sights.
Schools within 40 kilometres of Gaza are closed, and those living within seven kilometres of the strip have been told to stay home.
In Gaza, about 400 angry mourners braved the streets to bury Jabari.
Tension with Egypt
The Israeli offensive came hot on the heels of efforts by Egypt to secure a ceasefire. Egypt has now recalled its ambassador to Israel.
US president Barack Obama has spoken to both the Israeli and Egyptian leaders amidst the escalating crisis.
He reiterated Israel's right to defend itself, but urged Israel to make every effort to avoid civilian casualties.
Egyptian president Mohamed Mursi made a televised address to the nation, saying Israel's attacks on the Gaza Strip were "unacceptable" and would lead to instability in the region.
"We are in contact with the people of Gaza and with Palestinians and we stand by them until we stop the aggression and we do not accept under any circumstances the continuation of this aggression on the Strip," he said.
"The Israelis must realise that this aggression is unacceptable and would only lead to instability in the region and would negatively and greatly impact the security of the region."
The UN Security Council has held an emergency meeting to discuss the attacks, calling for an end to the violence but taking no other action.
Indian ambassador Hardeep Singh Puri, president of the 15-nation Security Council, said council members had only agreed to issue a communiqué stating that an emergency meeting took place and other procedural details.
"All the statements that I heard resonated with one message - that the violence has to stop, there has to be de-escalation," he said.
Arab nations had wanted the council "to condemn that barbaric attack" by Israel and "send a strong message to call for a cessation of hostilities", said Sudan's UN envoy Daffa-Alla Elhag Ali Osman, chairman of the Arab bloc at the UN.
But the United States strongly defended the actions of its key Middle East ally.
Highlighting Israel's claim that at least 768 rockets had been fired from Gaza this year, US ambassador Susan Rice told the security council: "Israel, like any nation, has the right to defend itself against such vicious attacks.
"There is no justification for the violence that Hamas and other terrorist organisations are employing against the people of Israel. We call on those responsible to stop these cowardly acts immediately."
Ms Rice, a frontrunner to become the next US secretary of state, said the rocket attacks were harming efforts to end the Middle East conflict and create a Palestinian state.
"Hamas claims to have the best interests of the Palestinian people at heart, yet it continues to engage in violence that does nothing but set back the Palestinian cause," she said.
"Attacking Israel on a near daily basis does nothing to help Palestinians in Gaza nor to move the Palestinian people any closer to achieving self determination and independence."
'Death, destruction, trauma'
Only the Palestinian and Israeli ambassadors were allowed to address the meeting on top of the council envoys.
Palestinian envoy Riyad Mansour told the council that a child of 11 months, two other children and a pregnant 19-year-old woman were among those killed in the attacks.
"Death, destruction, trauma and terror are being rained upon our people before the eyes of the world," he said.
"The international community must act to bring an end to Israel's illegal policies and practices against the Palestinian people."
Mr Mansour said the attacks were linked to the Palestinian application for observer status at the United Nations, which is due to be voted on by the General Assembly on November 29.
Israel's UN ambassador Ron Prosor said: "The goal of Israel's operation is clearly defined - to remove a strategic threat to Israeli citizens."
He told the council that Israel would not play "Russian roulette with the lives of our citizens".
"Hamas has turned Gaza into a haven and a breeding ground for global terrorist organisations," he said.