A special cabinet meeting ended with agreement to increase security efforts but not launch a military strike.
The suicide attack by a 21-year-old militant from the Islamic Jihad faction, which killed nine people at a crowded food stand in Tel Aviv, failed to elicit condemnation from the hardline Hamas government.
Prime Minister designate, Ehud Olmert, also authorised the army to step up its activities and carry out targeted killings against "all those involved in terrorism", including Hamas and Palestinian government officials, public radio said.
However, he stopped short of ordering a full-scale operation in the wake of the blast.
Israeli authorities would also harden restrictions on illegal Palestinian workers in Israel and those who drive them to their jobs, and seal even more hermetically the borders with the Gaza Strip and West Bank, the radio added.
Troops have arrested the father of the bomber while a further 38 Palestinians were rounded up overnight, security sources said.
Israeli government spokesman Ranaan Gissin raked Hamas over the coals for "the fact that they allow other terrorist organisations to carry out these horrendous terrorist attacks".
"We are in a war and we are taking all the necessary steps to defend ourselves like US troops are doing in Iraq," he said.
Infrastructure Minister Ronni Bar-On branded the Palestinian Authority a "terrorist entity" that "should be treated as such".
"We have innumerable means at our disposal and have a number of potential targets," he said.
Another official said Israel put full responsibility for the attack on the shoulders of Hamas because of its failure to condemn the bombing, in contrast to the practice of the former Fatah-dominated administration.
The move to increase security came as Israel buried five of the victims of the attack.
Israel, poised for further possible attacks during the Jewish Passover festival, has deployed reinforcements on all major highways and the border with the occupied West Bank.
US response
US President, George W Bush, deplored the suicide bombing and reiterated his call for a two-state solution to the conflict, despite little indication of peace overtures from Israel and the Hamas administration.
President Bush said "I strongly deplore the loss of innocent lives and the attack on the folks in Israel yesterday. Our goal is to have two states living side by side in peace."
In the wake of the attack, key donor Japan is considering whether to join a long list of countries which have suspended direct aid.