In response, Hamas' armed wing warned Jabari's assassination ''had opened the gates of hell'' and vowed its militants would ''continue the path of resistance''.

Israeli Prime Minister Benjamin Netanyahu warned that the military was ''prepared to expand'' its operation.

The IDF said its actions were part of a wider Israeli operation against militant groups and weapons sites in the Hamas-run Gaza Strip, and were prompted by a wave of rocket attacks against Israel.

Gaza's health ministry said 10 civilians had been killed, including two young children - an 11-month-old and a six-year-old - while at least 45 people had been wounded, 10 of them in critical condition.

There were scenes of chaos at Shifa Hospital in Gaza City, as dozens of seriously injured patients were carried in, while ambulances sped off to collect more casualties.

In southern Israel, residents have been ordered to stay in bomb shelters in preparation for an expected surge in rocket attacks from Gaza. Schools in a 40-kilometre radius of the border have closed.

Hamas, an Islamist movement considered a terrorist group by Israel, the US and the European Union, has appealed for help from the new Muslim Brotherhood leaders of Egypt.

Egyptian President Mohamed Mursi recalled the country's ambassador to Israel and called for an urgent meeting of the Arab League.

Egyptian Foreign Minister Mohamed Kamel Amr called on Israel to stop the strikes immediately, warning any further escalation from Israel ''could have negative repercussions on the security and stability of the region''.

The US threw its weight behind Israel.

''We support Israel's right to defend itself, and we encourage Israel to continue to take every effort to avoid civilian casualties,'' US State Department spokesman Mark Toner said.

''We strongly condemn the barrage of rocket fire from Gaza into southern Israel, and we regret the death and injury of innocent Israeli and Palestinian civilians caused by the ensuing violence,'' he added. ''Hamas claims to have the best interests of the Palestinian people at heart, yet it continues to engage in violence that is counterproductive to the Palestinian cause.''

Thirteen rockets fired from Gaza into southern Israel had been intercepted by the country's missile defence system, the IDF spokesperson said, tweeting with tag #PillarofDefense.

''We recommend no Hamas operatives, whether low-level or senior leaders, show their faces above ground in the days ahead,'' the spokesman said.

Saeb Erekat, a member of the Palestine Liberation Organisation's executive committee and chief Palestinian negotiator, condemned the attacks as an attempt to ''initiate a bloody escalation''.

''This exposes that Israel has an agenda for war but not for peace.''

Israeli Defence Minister Ehud Barak said Israel was not interested in engaging in war, but that Hamas' provocation over the past few days had forced it to act.

One Gaza resident, a doctor, posted on her Facebook page as the bombardment continued: ''Gaza is under extensive Israeli military attack … the hospitals are already lacking essential emergency medications, and citizens were called for blood donation, we do not have power … we expect more escalation.''

The video of Jabari's assassination was posted on YouTube by the IDF. Just 14 seconds long, it is shot from the air, following a car along a street before a missile strike all but obliterates it.

Jabari is the most senior Hamas operative to be killed by Israel in almost four years, since Operation Cast Lead, its three-week assault on Gaza, left about 1400 Palestinians dead.

He was widely believed to have been intimately involved in the Hamas takeover of Gaza in 2007, and played a key role in overseeing the imprisonment of Israeli soldier Gilad Shalit, who was snatched by Palestinian militants while on a patrol near the Gaza Strip in 2006 and held in secret locations in Gaza until his release in October 2011, in return for the release of 1027 Palestinian prisoners.

In a rare public appearance, Jabari escorted Shalit to the Rafah crossing with Egypt as part of the prisoner exchange.

Israel's air strikes have prompted anger, fear and panic in Gaza, with residents anticipating a prolonged Israeli campaign. Some are stocking up on essentials, while others are crowding outside the hospital and morgues in a vigil for the injured and dead.

In Australia, the Department of Foreign Affairs and Trade reissued its travel advisory for Israel and the Gaza Strip. The travel advisory has not been upgraded, but it contains new information about the attacks.

Australians have been urged to exercise a high degree of caution in Israel overall, while travellers warned to reconsider their need to travel in Bethlehem, Ramallah and Jericho, and have been advised not to travel in the Gaza Strip, including surrounding areas, and the remainder of the Israeli-occupied West Bank.

''We strongly advise you not to travel to areas around the Gaza Strip in southern Israel due to the possibility of mortar and rocket fire,'' the advisory says. ''A significant escalation occurred in October 2012. A further escalation may occur following the commencement of Israeli military operations against the Gaza Strip on 14 November 2012.''

Australians or their families in need of emergency assistance have been urged to call the 24-hour consular emergency centre on 1300 555 135 within Australia, or +61 2 6261 3305 from outside Australia. With AFP