After five straight days of punishing air attacks, Israel rejected a proposal for a 48-hour cease-fire in its military onslaught in Gaza on Wednesday, saying it would maintain pressure on Hamas. But it did not rule out future diplomacy and was open to ways of increasing humanitarian aid.

The decision was announced after a security cabinet meeting here.

The Israeli air strikes on Gaza continued on Wednesday, and at least 20 more rockets were fired by Hamas militants in reprisal into southern Israel, including three that landed in the city of Beersheba. Mark Regev, the spokesman for Prime Minister Ehud Olmert, said earlier that the country’s leaders “view it as important to keep up the pressure on Hamas.”

“We cannot give them a respite to rearm and regroup,” he said. “We need a real, sustainable solution, not a Band-Aid.” But he added that Israel would still explore ways to expedite humanitarian aid to Palestinian civilians in Gaza and would also explore a broader diplomatic effort to achieve a lasting cease-fire.

He and other officials said Israel was continuing to talk to American and European leaders about finding a longer-term diplomatic solution.

The idea of a 48-hour cease-fire emerged from a conversation between Foreign Minister Bernard Kouchner of France and Defense Minister Ehud Barak of Israel. It was supposed to establish at least a temporary pause in the fighting that would allow humanitarian relief to be delivered to the besieged coastal strip.

“The leading option right now is still a ground invasion, but the target of this operation is an improved cease-fire, and if that can come without the invasion, fine,” a close aide to Mr. Barak said Tuesday, speaking on the condition of anonymity because he is not Mr. Barak’s authorized spokesman. “But, of course, Hamas has to agree, and there has to be a mechanism to make it work.”

On Wednesday, rockets fired by Hamas militants struck targets more than 20 miles from Gaza, displaying greater range than earlier in the conflict. In Beersheba, one hit an empty school, according to news reports. Schools in Beersheba were ordered closed Tuesday because of an earlier missile strike. The Israeli military says that, while some Hamas rockets are home-made, the longer-range missiles are more sophisticated and are smuggled into Gaza.

Israeli warplanes bombed tunnels along Gaza’s border with Egypt which provide crucial supply lines. The crump of bombing could be heard from the Egyptian side of the frontier.

With Gaza’s food and medical supplies threatened by the conflict, a British government minister, Douglas Alexander, said aid was “desperately needed.”

“The human cost of this conflict is unacceptable and the humanitarian situation is getting worse by the hour,” said Mr. Alexander, the international development secretary, as he announced a $10 million emergency aid package on Wednesday.

In Cairo, a meeting of foreign ministers from the 22-member Arab League began amid calls by some Arab leaders for Palestinians to end disputes between Hamas in Gaza and the Fatah movement led by Mahmoud Abbas, the president of the Palestinian Authority, in the West Bank, according to news reports.

The latest European diplomacy began Tuesday when Mr. Kouchner met with his European Union colleagues over the Gaza crisis and called publicly for a permanent cease-fire. A similar call came from the so-called quartet of powers focused on the region — the United Nations, the European Union, the United States and Russia.

President Bush and Secretary of State Condoleezza Rice made phone calls to Israeli and Arab leaders to explore prospects for halting the fighting. They emphasized that any cease-fire should be “durable and sustainable,” compelling Hamas to end its rocket attacks, a State Department spokesman said.

“That is different from the cease-fire that existed in the last six months,” said the spokesman, Gordon Duguid, noting that Hamas had routinely violated the previous agreement by firing rockets into southern Israel.

The flurry of diplomacy appeared to be mostly byplay in Jerusalem and Gaza, as Israeli officials spoke of a continuing and expanding military operation, and Hamas vowed to step up its resistance. It was also clear that the number of targets available from the air was declining, making the likelihood of a ground offensive greater.

In Gaza, Hamas militants issued a taped statement vowing revenge for those killed in the Israeli air raids since Saturday and warning that a ground invasion would prove painful for Israel. Palestinian officials say that more than 370 people have been killed, among them, the United Nations says, at least 62 women and children and an unknown number of civilian men. Two sisters, ages 4 and 11, were killed in a strike in the north as concern was growing around the world that the assault was taking a terrible toll on civilians.

“It would be easier to dry the sea of Gaza than to defeat the resistance and uproot Hamas, which is in every house of Gaza,” said the statement from the military wing of Hamas. It was played on Hamas’s television station, which had been shut down by an Israeli missile but went back on the air by broadcasting from a mobile van. The statement added that if there was a ground invasion, “the children of Gaza will be collecting the body parts of your soldiers and the ruins of tanks.”

Israeli warplanes, returning repeatedly to the same section of Gaza City overnight, pummeled the main government complex with about 20 missiles, residents said Tuesday. The building had been evacuated since the start of the operation on Saturday, which also hit nearly all of Hamas’s security complexes, its university and other symbols of its sovereignty and power.

The Nakhala family, which lives next to the compound, was inspecting the damage on Tuesday morning and recounting the utter fear and panic they all felt as the missiles hit.

“We have no shelters in Gaza,” said the father, Osama Nakhala. “Where shall we go? I also have to worry about my mother, who is 80 years old and paralyzed.”

His 13-year-old son, Yousef, was with him. When asked his view of the situation, Yousef took an unusual stand for someone in Gaza, where Israel is being cursed by most everyone. “I blame Hamas. It doesn’t want to recognize Israel. If they did so there could be peace,” he said. “Egypt made a peace treaty with Israel, and nothing is happening to them.”

His brother Amjad, 16, disagreed and blamed the Palestinian president in the West Bank, Mahmoud Abbas, saying that he had sided with Israel.

Gaza City was entirely without electricity for the first time, the result of an air attack that hit the system’s infrastructure. Repair workers said they were afraid to work because of the possibility of more raids.

The few open bakeries and grocery stores had lines stretching outside as people tried to stock up. But essentials, like diapers, baby food, bread, potatoes and fresh vegetables, were in short supply and costlier than normal.

Israel sent in about 100 trucks with emergency supplies of food and medicine, the military reported.

At the Hassouna Bakery near Shifa Hospital, about 100 men and 50 women waited in separate lines to buy bread. Amal Altayan was telling others in the line that she kept her cellphone in her pocket so that if an Israeli missile destroyed her house she would be able to phone for help. The other women mocked her, saying that if a missile hit her house, she would be gone. Showing familiarity with the kind of knowledge circulating in Gaza these days, Ms. Altayan replied, “It depends. If it is an F-16 I will turn into biscuits, but if it is an Apache I may have a chance.”

Osama Alaf, 41, said he spent four hours waiting in line to buy bread. “I bought flour until now,” he said. “I don’t have cooking gas, but I make a fire out of cartons and paper and make bread that way.” Asked whom he blamed, he said, “Israel, which is slaughtering us, and whoever is cooperating with Israel, like Egypt.”

Anger at Egypt has grown across the Arab and Muslim worlds because it has declined to open its border with Gaza and is seen as cooperating with Israel.