Foreign Minister Silvan Shalom said on Monday that Israel's security cabinet had approved retaliation plans.
"We will do all we can to strike at the attackers," he said.
The move could trigger a new spiral of violence that may bury hopes stirred by Israel's pullout from Gaza in September after a 38-year occupation.
The Israeli army said it had also tightened restrictions on Palestinian movement in the West Bank and carried out incursions into the area.
Islamic Jihad said it had carried out the bombing to avenge Israel's recent killing of its senior members.
Mobile phone signals
Gaza-based leaders of the group could not be reached on their mobile phones.
"It will be a show of strength but not something that will get out of control"
Israeli security official
Israeli forces are believed to use mobile phone signals to pinpoint the whereabouts of such leaders to carry out air strikes.
Israeli security sources said Israel wanted to deal a heavy blow to Islamic Jihad.
But they said the response would be tempered to avoid drawing in Hamas, a more powerful Palestinian resistance group that has largely restrained itself during the period of calm agreed upon in February this year.
Bomber's family arrested
"It will be a show of strength but not something that will get out of control," one Israeli security official said.
Shalom said Israel had no plans to re-enter Gaza, but ground operations would focus on the northern West Bank.
Israeli occupation forces had earlier detained the father and three brothers of a Palestinian bomber in a raid on the West Bank village of Alar, near Tulkarim.
The arrests came a day after Lutfi Amin Abu Saada, 21, blew himself up at a shopping mall in the coastal town of Netanya, killing five Israelis.
Israel says demolishing bombers'
homes acts as a deterrent
Israeli military sources and Palestinian security officials said the four were detained at the family home in the village of Alar in the northern West Bank at daybreak.
The bomber's father, Amin Abu Saada, said on Monday that he had no idea about his son's links to Islamic Jihad, saying the first thing he knew about what had happened was when people began to converge on his home to offer condolences.
Aljazeera's correspondent in Palestine said Israeli forces also detained four other Palestinians in the village.
Six others, mostly Islamic Jihad members, were detained elsewhere in the West Bank.
Israel's Defence Minister Shaul Mofaz is seeking legal approval to reverse a ban on demolishing the family homes of bombers, saying that such a measure has a substantial deterrent effect.