Israel's Cabinet has decided to step up its military offensive against the Palestinians in response to a fresh suicide bomb and shooting attack that left 13 Israelis dead and more than 100 wounded.

Within hours of the two attacks, Israel launched an air and sea attack on Palestinian leader Yasser Arafat's showpiece headquarters in Gaza, completely destroying the building where Mr. Arafat used to greet world leaders. But the destruction of the greatest symbol of Palestinian authority was apparently considered an insufficient response for Israel's Cabinet. In its regular session, it backed an intensification of military actions in the West Bank and Gaza Strip.

An Israeli government official says the response to Palestinian attacks would be "in line with strategy already approved: continuous operations aimed at stopping the attacks."

There seems little hope of the violence ending soon, but Israeli Prime Minister Ariel Sharon says he will do everything in his power to halt the conflict. While saying he considers that Israel is now at war with the Palestinians, he has offered to consider a cease-fire without waiting for a calm period of at least seven days, a condition he has always insisted on in the past.

Jerusalem Mayor Ehud Olmert, speaking at the scene of the bombing, said the international community should stop criticizing Israel for defending itself. He said it is very easy to give advice from another part of the world. "It is entirely different when you have to face these people right here and these people do not listen to all these compromises and all these advises and all these analyses of political complications," Mr. Olmert said. "They want blood, and they want Jewish blood, and they want it as much as possible and that is what they are after."

Prime Minister Sharon says he welcomes a planned visit to the region later this week by U.S. Special Envoy Anthony Zinni.

The retired Marine Corps general is expected to call for the two sides to implement a cease-fire agreement mediated last year by the head of the Central Intelligence Agency, George Tenet.