Gaza/Tel Aviv - Israel rejected calls by the United Nations and European Union for an immediate ceasefire and instead prepared for what could be "long weeks of combat," as a ferocious air offensive against Hamas in the Gaza Strip entered its fourth day Tuesday.

Caretaker Israeli Prime Minister Ehud Olmert said the air campaign, which has seen close to 400 airstrikes on Hamas targets in Gaza in just four days, was only the "first" of a "series" of phases of the offensive.

Ground troops have massed outside Gaza since Sunday.

At least 11 people died in the latest airstrikes, bringing the the total number of Palestinian killed since Operation "Cast Lead" started Saturday to more than 369, the highest toll by far in decades of Israeli-Palestinian fighting.

At least 1,700 have been injured, Gaza emergency services chief Mo'aweia Hassanein said.

Four Israelis, including two Arabs - a Druze soldier and a Bedouin construction worker - have also been killed and dozens injured in rocket and mortar attacks.

Olmert's spokesman, Mark Regev, in response to a question by Deutsche Presse-Agentur dpa whether Israel was willing to accept an immediate new truce, said that it wanted no "instant fix" that would only temporarily end rocket and mortar attacks from the strip.

Defence Minister Ehud Barak meanwhile said the offensive's objectives were not only to curb rocket and mortar attacks from Gaza against southern Israel, but also to deal a "forceful blow" to Hamas and "fundamentally change the situation in Gaza."

He reiterated the offensive would continue until these goals were achieved. While Regev said he was unable to say how long this would take, Barak's deputy, Matan Vilnai, said Israel was prepared for "long weeks of combat." Hamas, Vilnai told Israel Radio, still had several hundreds of rockets.

Hamas said it was unfazed. The onslaught against it only made it "more determined to respond," spokesman Fawzi Barhoum said.

He warned that Israel would not succeed in toppling the Hamas regime in Gaza, pointing out that its 2006 war with Hezbollah had only strengthened the Lebanese radical Shiite movement.

Barhoum condemned the current Israeli air campaign as "genocide."

Most of the dead were members of Hamas' security forces and armed forces, but according to UN officials, at least 62 were women and children. They said they did not know how many of the men killed were civilians.

The latest civilian deaths included two sisters, aged 4 and 11, killed instantly when an Israeli missile struck the donkey cart they were riding north of Gaza City.

Seven Palestinians died when Israeli F16 fighter jets bombed the house of a Hamas commander in the same area. The house was empty, since Hamas has evacuated all of its buildings since the campaign started Saturday. According to Palestinian security officials, the dead were neighbours and bystanders. Israel also again bombed Hamas' Gaza City government headquarters, housing several ministries and the office of de-facto prime minister Ismail Haniya, reducing parts of it to rubble.

A defiant Hamas deepened its rocket attacks into Israel late Monday, for the first time ever reaching Israeli communities within a range of 30 kilometres from the strip, including the coastal town of Ashdod. Two Israelis were killed, including an Ashdod woman unversed in how to take cover who fled her car to hide in a bus stop, which was later punctured with shrapnel.

Israel launched the offensive one week after a fragile, six-month truce mediated by Egypt expired on December 19 and Hamas announced it would not extend it under the same terms. During that week, Hamas as well as the Islamic Jihad and other militant factions launched more than 180 rockets into southern Israel.

Since the truce first began disintegrating in early November, Israel has reimposed its near-total closure of the Gaza Strip, allowing in only sporadic shipments of humanitarian supplies about once a week.

It has allowed in aid more frequently since the offensive got under way, with Barak authorizing the entry for the third day running of several dozen trucks.

Some 109 trucks with medical supplies and basic food products such as flower, sugar, rice and animal feed donated by Jordan, Egypt and international organizations including the UN entered through Israel's border crossing of Kerem Shalom Tuesday, Major Peter Lerner, a Defence Ministry official, told dpa.

Five Turkish-donated ambulances were also sent in, he said.

The shipment came after UN Secretary General Ban Ki-moon urged Israel to keep Gaza's borders open to aid.

For the first time since the offensive began and after coming under internal pressure, Hamas allowed the transfer to Egypt of 57 seriously injured Gazans late Sunday and reportedly allowed the transfer of more on Monday.

Gaza's hospitals have had difficulty coping with the high casualty toll and some 300 critically injured people are said to need urgent transfers outside the strip.

Lerner said one seriously injured Palestinian was transferred to a hospital in Israel Sunday, but Israel had not received any requests for more transfers from Palestinian officials in Gaza.

Both Ban and Brussels, in separate statements, called for an immediate end to hostilities, and the UN under secretary general for humanitarian affairs accused Israel of using "excessive force."