"We will not make any discounts for terror groups, and the cease-fire will not prevent us from targeting them," Peretz said following a security assessment with senior defense officials, including outgoing IDF chief of General Staff Lt.-Gen. Dan Halutz.
Despite Peretz's harsh response, however, defense officials estimated that the IDF would not launch any major operations in response to the attack on Eilat.
Earlier, Israel's first Arab minister, Ghaleb Majadle (Labor), condemned on Monday the "loss of life" in the suicide bombing that took place earlier in Eilat, saying that "such attacks won't do anything for the peace process, and will only drag down talks."
"We need to do everything possible to ensure that these things won't happen, to ensure a better future for us all," Majadle said.
"We all want peace," he continued, adding that he believed that eventually the Palestinians would unite behind the need for negotiations.
In contrast to Majadle's comments, Hamas spokesman Fawzi Barhoum defended the suicide attack as legitimate "resistance" against Israel.
Barhoum called the attack a "natural response" to IDF policies in the West Bank and Gaza Strip, as well as its ongoing boycott of the Hamas-led Palestinian Authority government.
"So long as there is occupation, resistance is legitimate," he said.
He also said attacks on Israel were preferable to the recent bout of Palestinian infighting in Gaza. "The right thing is for Fatah weapons to be directed toward the occupation, not toward Hamas," he said.
Meanwhile, the Islamic Jihad, which claimed responsibility for the attack together with two other groups, posted a statement on its Web site Monday saying that it had engineered the bombing in an attempt to "focus Palestinians' attention away from killing each other," Sky News reported.
Elsewhere, Prime Minister Ehud Olmert said in a Kadima faction meeting that for "a long time, Israel [had] enjoyed the illusion of quiet."
Olmert cautioned, however, that it was just that - an illusion - adding that in recent months, Israel had prevented numerous terror attacks.
Olmert extended his condolences to the families of the victims, and said that he had spoken with the mayor. "I believe Eilat will overcome this blow, and remain a happy city," Olmert said.
The prime minister said he would consult security officials, and only after all relevant intelligence had been collected would the IDF decide on a course of action.
Government spokeswoman Miri Eisen told Sky News that despite the fact that three terror groups had claimed the bombing, Israel had no final confirmation of responsibility, and therefore it was "premature" to discuss any possible Israeli reaction to the attack.
Eisen stressed that Israel was under "constant attacks and threats," and that if the number of terror attacks had recently declined, it was due to the diligence of the nation's security forces.
"Israel is always on guard," Eisen said. "We try to stop bombers before they reach their targets." Eisen added that individual bombers were supported by an entire terror network.
Meir Yitzhak Halevi, mayor of Eilat, called the fact that suicide bombers had managed to infiltrate the city "very disturbing," and said that he hoped that city officials would soon have all the information necessary to address the threat.
Vice Premier Shimon Peres spoke with Halevi on the phone after the attack.
"Eilat was, and will remain in the future, a city of peace and tourism. All means necessary will be utilized to assure that this situation continues," Peres said.
The US administration on Monday strongly denounced the attack, saying such violence undermines Palestinian hopes for an independent state.
"Our condolences go out to the victims, their families and the people of Israel. We also condemn those Palestinian terrorist groups, including Hamas, that condone these barbaric actions," the White House said in a statement.
"The burden of responsibility for preventing terrorist attacks rests with the Palestinian Authority government," it added. "Failure to act against terror will inevitably effect relations between that government and the international community and undermine the aspirations of the Palestinian people for a state of their own."
French Foreign Minister Philippe Douste-Blazy said on Monday afternoon that France condemned the terror attack in Eilat.
"There is absolutely no reason that can justify such violent action," Douste-Blazy said.