US Republican presidential candidates could hardly contain their revulsion of the Islamic State (ISIS) after the jihadist group admitted responsibility for the horrific terrorist attacks in Paris on Friday night that killed at least 129 people.

The mild-mannered Ben Carson uncharacteristically erupted in fury and exclaimed "Destroy them [ISIS]!" while talking to reporters while Jeb Bush said, "We should declare war."

Sen. Marco Rubio said the world is now witnessing "a clash of civilisations" where it's "either they win or we win."

Sen. Ted Cruz said ISIS "is an evil that does not discriminate between French, German or American, Christian, Muslim or Jew, soldier, football player, or concert goer."

Carson learned about the mass killings in Paris on Friday after he delivered a speech at a Republican Party event in Orlando, Florida. Speaking to reporters, the former neurosurgeon said if he were president he would "destroy" the "global jihadist movement," MailOnline reported.

"There are those out there who have a thirst for innocent blood, in an attempt to spread their philosophy and their will across this globe," Carson said during a brief press conference.

"And we must redouble our efforts and our resolve to resist them, not only to contain them but to eliminate that kind of hatred in the world."

Asked how he would handle the ISIS threat if he were elected president, Carson replied: "I think America's involvement should be trying to eliminate them completely. Destroy them!"

Meanwhile, Bush said on Sunday that the United States should immediately declare war on ISIS, Newsmax reported.

"This is viewed as a law enforcement exercise by the Obama administration. We should declare war," Bush said on NBC's "Meet the Press." "Harness all the power that the United States can bring both diplomatically and militarily of course to be able to take out ISIS. We have the capabilities to do this. We just have to show the will."

Asked what steps the U.S. should now take to fight ISIS, Bush replied: "Declare a no-fly zone over Syria, directly arm the Peshmerga forces in Iraq, re-engage with the Sunni tribal leaders, embed with the Iraqi military, make safe zones in Syria, garner the support of our European allies, and the traditional Arab states. Lead!"

For his part, Rubio called the terrorist attacks in Paris a "wake up call." In a statement he issued on Saturday, Rubio said ISIS wanted to "overthrow our society" because of the ability of young girls to attend school and drive and America's freedoms of speech and religion, The Blaze reported.

"This is a clash of civilisations," he said. "And either they win or we win."

Meanwhile, Cruz said the ISIS "only goal is to murder those who do not submit to their vicious, totalitarian ideology," according to The Right Scoop.

What the U.S. needs to do, he said, is "to consult closely with our NATO allies who may be targeted for additional attacks. We need to immediately declare a halt to any plans to bring refugees that may have been infiltrated by ISIS to the United States. We need to redouble our efforts to prevent ISIS agents from penetrating our nation by other means."

For his part, Republican presidential frontrunner Donald Trump did not state his plan for ISIS but only commented that the terrorist attack in Paris might not have happened if French laws allowed for more people to carry guns, Bloomberg reported.

"The toughest gun laws in the world: Paris," Trump said during a campaign rally of about 8,000 people in Beaumont, Texas. "If they were allowed to carry—it would have been a much, much different situation."

Across the political divide, Democratic presidential frontrunner Hillary Clinton said the fight against ISIS must be led by the United States but cannot be fought by Americans alone, Bloomberg reported.

"I know America has to lead it but we cannot and should not do it alone," Clinton said at the Central Iowa Democrats Fall Barbecue in Ames, Iowa, on Sunday.