After filing to run in the New Hampshire Republican presidential primary, candidate Ben Carson attempted to clarify statements he made the day before likening refugees fleeing violence in Syria to "rabid dogs." (Reuters)

One of the front-runners in the Republican presidential race said Thursday he would “absolutely” want a database of Muslims in the country and wouldn’t rule out giving them special ID cards that noted their religion.

Another top candidate likened Syrian refugees — who are largely Muslim — to dogs. Some of them might be rabid, he said, which was reason to keep them all out.

And a third stood up in the Senate on Thursday and called for banning refugees from five Middle Eastern countries. He was explicit that the point was to keep Muslim refugees out while letting Christians from the same places in.

A week after terrorists tied to the Islamic State terrorist group killed 129 people in Paris, some Republican politicians have responded with the kind of rhetoric that another Republican — George W. Bush — explicitly avoided after the al-Qaeda attacks of Sept. 11, 2001. In the angry aftermath, Bush said that “Islam is peace” and that all Muslims should not be judged for the deeds of a few radicals.

But in this election — already defined by a suspicion of government and anger about immigration — the rhetoric on Muslims has become a dominant feature of the Republican response to the attacks. It also comes as 47 House Democrats joined with 242 Republicans on Thursday to pass a bill placing new security constraints on President Obama’s pledge to admit 10,000 Syrian refugees, most of whom would be Muslim.

House Speaker Paul Ryan spoke about the efforts from House Republicans to pass legislation pausing the refugee resettlement program. "It's a security test, not a religious test," he said. (AP)

Some Republican presidential candidates have said they would go further and argue that all Muslims should bear greater scrutiny because it is too difficult to tell which ones are the radicals.

“If there’s a rabid dog running around in your neighborhood, you’re probably not going to assume something good about that dog, and you’re probably going to put your children out of the way,” retired neurosurgeon Ben Carson said Thursday in Mobile, Ala.,when he was asked about Syrian refugees. “It doesn’t mean that you hate all dogs by any stretch of the imagination, but you’re putting your intellect into motion.”

Such rhetoric from candidates who would lead the Republican Party has been loudly condemned by Muslim groups and politicians.

“It’s unacceptable, and if we have somebody running for president they’re going to be president for all people,” said Rep. André Carson (D-Ind.), one of two Muslim members of Congress. “We can’t have candidates painting a group of people with a broad brush, and that’s exactly what they’re doing.”

The growing suspicions about Muslims have not been limited to presidential candidates. In one particularly vivid example, Sid Miller (R) — the elected agriculture commissioner in Texas — likened Syrian refugees to rattlesnakes. “Sure some of them won’t [bite], but tell me which ones so we can bring them into the house,” Miller wrote in a Facebook posting.

The suspicions have also not been limited to Republicans. Earlier this week, the Democratic mayor of Roanoke, Va., cited the internment of Japanese Americans in camps during World War II, under suspicion because of their race, as a positive lesson for dealing with Syrian refugees.

Which governors want to keep Syrian refugees out of their states

And Hillary Clinton’s top political patron, entertainment titan Haim Saban, called for “more scrutiny” of Muslims for ties to terrorism. Clinton’s camp did not respond to a request for comment about his remarks.

Saban later issued a statement saying that he regretted making a “religious distinction as opposed to a geographical one,” saying he favors scrutiny of people from countries where the Islamic State has strongholds.

On the Syrian refugee issue, the Republican presidential candidates favor going further than the House bill, by blocking all or some of the migrants — though, so far, the Paris attackers who have been identified have all been European.

Donald Trump, who has suggested closing down mosques and increasing surveillance of Muslims, said in an interview with Yahoo News published online Thursday that “we’re going to have to do certain things that were frankly unthinkable a year ago.”

When pressed on whether such measures might include tracking Muslim Americans in a database or noting their religious affiliations on identification cards, Trump said: “We’re going to have to — we’re going to have to look at a lot of things very closely. We’re going to have to look at the mosques. We’re going to have to look very, very carefully.”

Later Thursday, Trump told NBC News that he would “certainly” and “absolutely” create a database of Muslims in the United States, although it was unclear whether this system would track only newcomers to the country or all Muslims living in the country.

“There should be a lot of systems beyond databases,” Trump said. “I mean, we should have a lot of systems.”

Other Republican candidates have suggested that the United States might be in conflict with Islam itself.

Carson, for instance, has said that he would not support a Muslim for president because that faith might not be “consistent” with the U.S. Constitution. In the aftermath of the Paris attacks, Ohio Gov. John Kasich recently proposed a new federal agency to spread “Judeo-Christian Western values” in the Middle East.

And Sen. Marco Rubio (Fla.) said the attacks were part of a “clash of civilizations” — essentially casting the Paris attackers as products of Muslim society rather than a radical group apart from it.

“I don’t understand it,” Rubio said when asked about Clinton’s refusal to describe the terrorists’ ideology as “radical Islam” to avoid offending Muslims. “That would be like saying we weren’t at war with the Nazis, because we were afraid to offend some Germans who may have been members of the Nazi Party but weren’t violent themselves.”

Two other candidates — Sen. Ted Cruz (Tex.) and former Florida governor Jeb Bush — suggested this week that the United States should accept Christian refugees from Syria but not some or all of the Muslim refugees. That is in contrast to the new Republican House speaker, Paul D. Ryan (R-Wis.), who said there should be no religious test.

The two candidates’ argument, however, was that a Christian refugee is by definition more deserving and less risky.

“There is no meaningful risk of Christians committing acts of terror,” Cruz said earlier this week. Cruz introduced a bill that would bar refugees from five countries, including Syria, with an exception carved out for groups that were victims of genocide. On Thursday, Democrats blocked the bill.

The approach contrasts sharply with Bush’s brother in 2001. George W. Bush visited a Washington mosque six days after the 9/11 attacks and later gave an address to Congress that urged tolerance toward Muslims.

“The terrorists are traitors to their own faith, trying, in effect, to hijack Islam itself,” the president said. “The enemy of America is not our many Muslim friends. . . . Our enemy is a radical network of terrorists and every government that supports them.”

George W. Bush and his advisers were trying to tamp down anti-Muslim backlash in the United States and to counter a narrative from the terrorists themselves — that Islam and the West were at war. Bush’s version tried to put the United States and the bulk of the world’s Muslims on the same side of the fight, defending civilization against al-Qaeda’s barbarity.

That message seems to have sunk in: A recent Bloomberg poll, taken after the Paris attacks, showed that 61 percent of Republicans and 76 percent of Democrats agreed with the statement that “Islam is an inherently peaceful religion, but there are some who twist its teachings to justify violence.”

“If you buy into [the terrorists’] narrative, then I don’t know how you win,” said Michael Gerson, a former Bush speechwriter and a columnist for The Washington Post. “So the most basic point that we were making . . . was that what we were seeing in al-Qaeda was an aberration within Islam.”

Clinton, who is a strong favorite to win the Democratic nomination, said in a foreign policy speech Thursday that “we cannot allow terrorists to intimidate us into abandoning our values and our humanitarian obligations.”

“Turning away orphans, applying a religious test, discriminating against Muslims, slamming the door on every Syrian refugee — that is just not who we are,” she said.

But public opinion is not with her. The same Bloomberg poll released this week showed that 53 percent of Americans and 69 percent of Republicans opposed accepting any Syrian refugees at all. Among Republicans, 24 percent said they support Trump for president.

“Feed our kids,” read one sign at a Trump rally in Massachusetts this week. “Not 10,000 refugees.”

Philip Rucker in Mobile; Jenna Johnson in Worcester, Mass.; Ed O’Keefe in Manchester, N.H.; and Katie Zezima and Sean Sullivan in Washington contributed to this report.