U.S. presidential candidates comment on the Paris shootings and bombings that killed at least 127 people and left dozens in a critical condition. (Thomas Johnson/The Washington Post)

The deadly rampage in Paris on Friday thought to have been carried out by the Islamic State has introduced a new dynamic into this country’s 2016 presidential campaign, increasing the pressure on candidates in both parties to project resolve and clarity about how they would deal with the threat.

The attacks, coming shortly after President Obama declared that the terrorist group had been “contained,” brought forth a torrent of criticism of his leadership from the large field of Republican contenders.

At the same time, they have stopped short of calling for more involvement of U.S. troops. The only specific proposal a handful of them have offered is to block Syrian refugees from entering the United States. In September, Obama announced that the United States would accept at least 10,000 refugees from the conflict over the next year.

“President Obama and Hillary Clinton’s idea that we should bring tens of thousands of Syrian Muslim refugees to America — it is nothing less than lunacy,” Sen. Ted Cruz (R-Tex.) said Saturday in an interview on Fox News Channel. He added that only Christian refugees should be allowed to come to this country.

The attacks in Paris also raised a question for Republican voters: Will they continue to be drawn to the bellicose rhetoric most exemplified by front-running political outsider Donald Trump, or turn instead toward the experience of some of the current and former senators and governors in the race?

“Foreign policy is a gateway issue, and this is the moment in which the gate’s got to be hit by all the candidates,” said Kori Schake, a foreign policy expert at Stanford University’s conservative Hoover Institution. “It is a commander-in-chief test.”

John R. Bolton, a conservative former diplomat, said that foreign policy is “a test of character and judgment.”

“It’s not enough to have candidates who can give good speeches their staff has written,” he said. “It’s not enough to have memorized talking points on a debate stage. You have to demonstrate that you have the ability to think through a range of issues on your own and confront crises that are not even imaginable.”

On the Democratic side, favorite Hillary Rodham Clinton’s record as secretary of state gives her an advantage, both in the party’s primary and in the general election — provided that she is not tagged with fostering the chaos in the Middle East that led to the rise of the Islamic State.

If the crowd that began lining up hours early on Saturday to attend a Trump rally in Beaumont, Tex., was any indication, the events in Paris brought new fervor to the staunchest supporters of his campaign, which recent polls show has been plateauing.

“After what happened last night, we need a leader that’s going to develop a plan and go in and do it,” said Mary Jane Avery, 61, of Burnet, Tex. “You can’t talk to those people. They are living on a different wavelength that we do not understand. And they just have to be wiped out.”

At the second Democratic presidential debate, candidates Hillary Clinton, Bernie Sanders and Martin O'Malley spoke about the attacks that left more than 100 people dead in Paris the night before the debate. (Sarah Parnass/The Washington Post)

Republican political consultant Alex Castellanos said Trump is the candidate who most speaks to the moment on a visceral level. “We want a president equal to our fears, big scary fears about holding the world together and survival,” said Castellanos, who is not affiliated with Trump’s campaign. “All of this has just been accentuated in the last 24 hours, now even more so. Now that strong leader is even more imperative.”

Trump — who said recently that he would “bomb the s--- out of” oil fields controlled by the Islamic State — opened his rally Saturday by leading the crowd of several thousand in a moment of silence in remembrance of the more than 120 people killed in the Paris attacks. Trump also erroneously asserted, as he has before, that Obama planned to allow 250,000 refugees into the United States.

“You have to be insane,” Trump said of resettling Syrian refugees. “Terrible.”

Trump said in late September that if he is elected, he will force all Syrian refugees to leave the United States. He has said that these refugees could be a terrorist army in disguise and that they cannot be trusted. Such comments have resonated with rally crowds nationwide and did so again in Texas on Saturday.

On the campaign trail, the contenders who have been lagging behind Trump and retired neurosurgeon Ben Carson have touted their credentials as they have offered condolences.

“All of those qualities that these insider candidates have that we devalued can now be their strength: I know what to do now,” Castellanos said. “This is grown-up time.”

Former Florida governor Jeb Bush, for instance, is the son and brother of former presidents whose legacies, for better or worse, were shaped by their foreign policy stances.

“This is the war of our time and we have to be serious in engaging and creating a strategy to confront and take it out,” Bush said in an interview Friday with conservative talk-radio host Hugh Hewitt.

Sen. Marco Rubio (Fla.), a foreign policy hawk who has made his time on the Senate Foreign Relations Committee a cornerstone of his case for winning the GOP nomination, said in an interview on Fox News Channel that he recognized the true nature of the Islamic State early.

“For more than a year,” Rubio said, “I’ve been talking about how they became the predominant jihadist group in Libya. How they’d use it to conduct attacks in the Sinai and eventually into Europe, as well.”

But while the Paris attacks are chilling evidence of the growth in the Islamic State’s sophistication and potency, there is no clear plan in either party as to how to handle it.

“There’s not one person — no one, not in the administration, not on the debate stage — that shows coherence as to what we should do. That person doesn’t exist,” said Steve Schmidt, who was an official in the George W. Bush White House and a top adviser to 2008 GOP presidential nominee John McCain. “The Republicans who criticize the administration — appropriately — for not having a strategy also don’t have a strategy.”

Johnson reported from Houston and Costa from Atlanta.