Mofaz, speaking on Israeli radio, also said he was seeking approval to resume a policy of demolishing the homes of bombers that Israel had suspended in February after the start of a truce with Palestinians.
The Israeli threat came as armed clashes broke out in the West Bank town of Jenin between Palestinian security forces and followers of the resistance group that carried out the bombing earlier on Monday in northern Israel.
Witnesses and security sources said the clashes had broken out on the margins of a demonstration called to "celebrate" the bomb attack outside a shopping mall in Netanya.
As they gathered outside the local headquarters of the security services, the demonstrators, who also included members of Al-Aqsa Martyrs Brigades, began chanting slogans denouncing the Palestinian Authority.
Exchanges of fire then broke out, the witnesses said, although there were no immediate reports of casualties.
Monday's blast, detonated by a bomber outside a shopping mall in the coastal town of Netanya killed five Israelis and wounded at least 40.
The Palestinian resistance group Islamic Jihad has claimed responsibility for the bombing and released a video purportedly showing the bomber with an assault rifle and rocket-propelled grenade launcher against the backdrop of the movement's flag, according to Reuters.
Speaking to Aljazeera earlier on Monday, Khidr Habib, a spokesman for Islamic Jihad, said the group neither rejected nor claimed responsibility for the bombing, but was awaiting confirmation from its military wing.
Emergency officials put the death toll at five and said 40 people were wounded, seven of them seriously.
A 21-year-old Palestinian was reportedly challenged by police when he tried to enter the mall.
Avi Sasson, deputy police chief in the area, said: "Two policemen at the scene pulled out their guns and ordered him to halt and to take his hands out of his pockets. At that stage, he blew himself up."
Ariel Sharon, the Israeli prime minister, cancelled political meetings and consulted his security chiefs on a military response, the second inside the Jewish state since Israel's withdrawal - after a 38-year occupation - from Gaza.
Mahmoud Abbas, the Palestinian president, condemned the bombing as a "terrorist attack". His office said he had "issued firm instructions to arrest those involved and those responsible ... and put them on trial".
Abbas' office issued a statement
condemning the bombing
But Habib said he believed that the attack "comes in the context of a natural reaction of the Palestinian people and resistance forces toward ongoing Israeli crimes".
He told Aljazeera: "These crimes have reached extreme limits and we can not remain silent. We will not stand motionless in front of Israeli oppression, as we reject being humiliated.
Our Palestinian people have offered many martyrs and would continue its efforts to give thousands of martyrs to defend our dignity."
"Our people will respond to these ongoing Israeli crimes.
Habib reiterated that the Islamic Jihad movement supports such operations as it is "in retaliation to ongoing Israeli crimes".
"The Israeli enemy has continued carrying out massacres, raids and crimes against our people disregarding the period of calm," he said.
"We have always reiterated our commitment to the period of calm.
"Sharon is the one whose commitment to the agreed period of calm should be questioned, not Palestinian resistance groups."
When asked about the Palestinian Authority's efforts to revive the peace process, Habib has said: "We are defending ourselves. We do not want to embarrass the Palestinian Authority or anyone else.
"Sharon is the one whose commitment to the agreed period of calm should be questioned, not the Palestinian resistance groups"
islamic Jihad spokesman
"If the world is concerned about calm in this area, it then should put pressure on the Israelis to halt its crimes and massacres against our people."
Palestinians have accused Sharon of stoking violence with sporadic military incursions in Palestinian areas and the continued expansion of Jewish settlements in occupied West Bank.