Israel's ferocious air offensive in the Gaza Strip entered its fourth day on Tuesday as it seeks to deal a "forceful blow" to Hamas radicals despite widespread international calls for a lasting ceasefire.

The Palestinian death toll in the fighting has reached 380 since Israel launched "Cast Lead," the highest toll by far in decades of Israeli-Palestinian fighting. Gaza officials reported more than 1,800 injured.

Meanwhile, Hamas stepped up rocket attacks with increasingly deeper strikes into southern Israel. Israel said the air assault was in response to Hamas missile attacks that intensified after a six- month truce ended this month.

The fighting continued to claim the lives of children. Two sisters, aged 4 and 11, were among those killed Tuesday after the donkey cart they were riding in Beit Lahiya, north of Gaza City, was hit by an Israeli missile.

Seven other Palestinians died when Israeli F-16 fighters bombed the abandoned house of a Hamas commander. According to Palestinian security officials, the dead were neighbours and bystanders.

A guard at a UN school in the southern Gaza Strip town of Khan Younis was also killed by shrapnel from missiles that targeted a nearby Hamas police station.

Israeli jets levelled the Gaza City compound housing official buildings and presidential headquarters used by Hamas since it's seizure of the Strip 18 months ago in a new round of airstrikes Tuesday night.

Israel made clear that it was prepared for a drawn out fight with Hamas and was in the advanced stages of preparing for a possible ground offensive. There were also reports that another call up of Israeli military reservists was in the works. Israeli Deputy Defence Minister Matan Vilnai said his country was prepared for "long weeks of combat" and warned the Hamas still had hundreds of rockets. Defence Minister Ehud Barak the Israeli goal was to deal a "forceful blow" to Hamas, and "fundamentally changing the situation in Gaza."

Large parts of Gaza City was plunged into darkness for a third uninterrupted night, while many apartment buildings were without water for as many days.

The Israeli army said it had destroyed as many as 40 tunnels under the border town of Rafah. The vast network of tunnels is used to smuggle goods and weapons into the Gaza Strip, circumventing a tight Israeli blockade.

Hamas remained defiant. The Israeli onslaught only made it "more determined to respond," spokesman Fawzi Barhoum said, warning that Israel would not succeed in toppling Hamas rule in Gaza.

Gaza militants reached deeper into Israel with rockets fired Tuesday night. Two upgraded Russian-type Grad rockets struck the southern city of Beersheba, in the first and furthest hit since Palestinian rocket attacks against Israel from the Gaza Strip began seven years ago.

An empty kindergarten in the city located around 40 kilometres from the Gaza Strip, was struck as well as an open area just to the south of when the rockets fell after darkness.

The greater range of the Hamas missile attacks was a cause for increased concern because about 1 million Israelis live in a 40- kilometre radius from the Gaza Strip, Police Spokesman Micky Rosenfeld told dpa.

Israel meanwhile rejected calls for a ceasefire by the United Nations, the European Union and France. An Israeli defence official said French Foreign Minister Bernard Kouchner had proposed Israel unilaterally halt its assault for 48 hours to give Hamas a chance to end its rocket and mortar attacks as well.

The United States blames Hamas for the violence and said a "sustainable" ceasefire will only be acceptable if the rocket attacks stop. "We don't want a ceasefire agreement that isn't worth the paper it's written on," said Gordon Johndroe, a White House spokesman. President George W Bush spoke with Palestinian President Mahmoud Abbas and Egyptian President Hosny Mubarak Tuesday about a possible truce.

A spokesman for Israel's caretaker Prime Minister Ehud Olmert said the country would not suspend its offensive before its goals were achieved. It would however work "energetically" with foreign governments and international organizations to allow a "constant flow" of aid into Gaza, he added.

EU foreign ministers holding an emergency meeting in Paris called for an immediate ceasefire so humanitarian aid can be funnelled into Gaza. "There must be an unconditional halt to rocket attacks by Hamas on Israel and an end to Israeli military action. The cessation of fighting should allow lasting and normal opening of all border crossings," the ministers said in a statement.

The diplomatic mediating group on the Middle East peace process, meanwhile, called for an immediate ceasefire that would be "fully respected" by Israel and Hamas and called on both sides to allow humanitarian missions into the Gaza Strip.

Palestinian President Mahmoud Abbas ordered all celebrations for the New Year and for next week's Greek Orthodox Christmas Day in Bethlehem cancelled Tuesday.

Egypt's leadership warded off criticism of its keeping its border with the Gaza Strip closed, insisting on strict implementation of previous truce agreements to assure border security.

Mubarak said his country will not fully open its border with the Gaza Strip unless Palestinian Authority or EU observers are in control of the crossing point. He explained that until then the borders will only be opened for humanitarian reasons.

Mubarak reiterated that "Egypt denounces the Israeli aggression over Gaza."

Thousands took to the streets across the world Tuesday to protest the Israeli airstrikes and call for an end to the violence. Dozens of Islamist students stormed a British compound in Tehran Tuesday night to protest the Israeli assault in the Gaza Strip, tearing down the British flag before police restored order, the official Iranian news agency IRNA reported.

In Morocco, main protests against Israeli airstrikes- in the form of marches and sit-ins - went ahead in Casablanca, Rabat, Kenitra and Meknes with demonstrators demanding an end to the airstrikes and decisive action by the international community.

The Singapore Foreign Ministry urged Israel and Hamas to exercise restraint and renew a truce that ended December 19.

The Lebanese government decided Tuesday to donate 1 million dollars to support the people of Gaza. In emergency session, the cabinet also announced that Wednesday would be an official day of mourning in solidarity with the people of Gaza. (dpa)