UPDATE 1: Airstrikes continue inside Gaza as world leaders step up their pleas for end to the violence.
Israel on Wednesday ruled out agreeing to a temporary truce in its offensive on Hamas in the Gaza Strip as world leaders stepped up calls for an end to the violence and warplanes pummelled Hamas targets.
"The proposition by the French Foreign Minister Bernard Kouchner for a unilateral temporary ceasefire is not useful as it is evident that Hamas will not stop firing rockets against Israel," a senior official said on condition of anonymity.
Israeli officials warned that the onslaught which has killed at least 373 Palestinians in its first four days could continue for weeks.
Hamas militants fired two rockets deep into Israel on Wednesday, both hitting near the desert city of Beersheva some 40 kilometres (24 miles) from the border of the Gaza Strip, the army said.
The Grad-type rockets caused no injuries or damage, the Israeli media said.
In Gaza City, the armed wing of Hamas claimed responsibility for the attacks, which mark the farthest yet that the militants' rockets have reached.
Another rocket fell near the town of Netivot, about 10 kilometres from the Gaza Strip but caused no injuries, said the Maguen David Adom, the Israeli equivalent of the Red Cross.
A rocket fired from the Gaza Strip late Tuesday slammed into an empty field in Beersheva, again without causing damage or casualties.
Gaza militants have been firing deeper into Israel in recent days and a spokesman for the armed wing of Hamas vowed on Tuesday rockets would be fired even further if Israel doesn't halt its bombardment of the Palestinian territory.
The militants have recently acquired military-grade projectiles with a longer range than the so-called Qassam rockets they manufacture themselves.
US President George W. Bush spoke Tuesday with Palestinian president Mahmud Abbas to discuss a "sustainable ceasefire."
"They agreed that for any ceasefire to be effective, it must be respected, particularly by Hamas ," White House spokesman Gordon Johndroe told reporters in Crawford, Texas.
The European Union separately called for a "permanent" ceasefire in and around the Gaza Strip, while the Middle East Quartet called for "an immediate ceasefire that would be fully respected."
The Quartet brings together the European Union, Russia, the United Nations and the United States.
But throughout the day, Israeli officials insisted the armed forces would press on with the offensive, which has sparked Muslim outrage and protests worldwide.
"What we want is not a ceasefire but a stop to terrorism," said President Shimon Peres.
Infrastructure Minister Benjamin Ben-Eliezer warned a ceasefire would allow Hamas "to regain strength, recover from the shock and prepare an even stronger attack against Israel."
"There is no reason that we would accept a ceasefire at this stage," he told AFP.
With tanks and troops massed on the Gaza border, the Israeli military said ground forces were ready to join what politicians have warned would be a prolonged offensive.
Israeli Prime Minister Ehud Olmert said the bombardment so far was "the first of several stages approved by the security cabinet," while deputy Defence Minister Matan Vilnai warned the offensive - one of Israel's deadliest against Gaza - could turn into "weeks of combat."
World leaders have expressed serious concern about the humanitarian situation in Gaza, a tiny, aid-dependent territory of 1.5 million which Israel has virtually sealed off since Hamas seized power in June last year.
Israel opened one of its crossings into Gaza for a third consecutive day on Tuesday, the defence ministry said, adding that a total of 179 truckloads of humanitarian supplies and 10 ambulances were delivered since the start of the military offensive.
Warplanes, meanwhile blew up dozens of tunnels along Gaza's border with Egypt, which Hamas used to smuggle weapons and bring in "terror activists," a military spokesman said in a statement. "These tunnels play a major role in supplying Hamas with the means of strengthening its ability to carry out terror," the statement said.
It said 30 additional targets were attacked on Tuesday, including rocket launchers, weapons manufacturing facilities and "armed terror operatives."
Four days of intensive bombardment have killed several senior Hamas officials and reduced much of the Islamist movement's infrastructure in Gaza to rubble.
Hamas has threatened to carry out suicide attacks inside Israel for the first time since January 2005.
Since the massive aerial attack was unleashed on Saturday, at least 373 Palestinians, including 39 children, have been killed and 1,720 wounded, Gaza medics say.
Israel's offensive followed days of rising violence after a tenuous six-month truce in and around Gaza ended on December 19; and ahead of early parliamentary elections in Israel due February 10.