Updated

A proposal to permit Syrian refugees into the United States has been met with an overwhelming opposition from Republicans in the wake of the Paris terror attacks, but two of the party's leading presidential hopefuls have expressed their contempt for it a notch louder.

Real estate mogul Donald Trump and Texas Sen. Ted Cruz have emerged as the country's leading voices of opposition to Syrian refugees and in support of ratcheting up the U.S.'s national security initiatives, following the terror attacks in Paris that killed 130 people and wounded hundreds more.

The Islamic State group has claimed responsibility for the carnage, elevating fears of attacks in the U.S. and prompting calls for new restrictions on refugees fleeing war-torn Syria.

Cruz has suggested that the U.S. only accept refugees from Syria who are Christian, despite the Middle Eastern nation being predominantly Muslim, and introduced to the Senate the Terrorist Refugee Infiltration Prevention Act of 2015.

"Given the existential nature and scope of the threat posed by radical Islamic terrorism, the limitations on our ability to screen the flood of refugees, and the obligations of our government to provide for the safety and security of all Americans," Cruz wrote in an opinion piece in the Washington Times. "[W]e simply cannot accept refugees from countries that have a significant terrorist presence until the terrorist threat has been eliminated."

For his part, Trump has mentioned closing down mosques across the country, listing American Muslims in a database and offering them a special ID.

"Nobody wants to say this and nobody wants to shut down religious institutions or anything, but you know, you understand it," Trump said on Fox News' "Hannity."

"A lot of people understand it. We're going to have no choice," he added.

Marci Hamilton, a Yeshiva University legal expert on religious liberty, said requiring Muslims to register appears to be a clear violation of the Constitution's protection of religious freedom.

"What the First Amendment does and what it should do is drive the government to use neutral criteria," Hamilton told the AP. "You can use neutral criteria to identify terrorists. What it can't do is engage in one-religion bashing. That won't fly in any court."

Former Florida Gov. Jeb Bush was the first Republican rival to condemn Trump's call for a Muslim database, calling the proposal "abhorrent."

"You're talking about internment, you're talking about closing mosques, you're talking about registering people, and that's just wrong," Bush said Friday on CNBC.

Bush, however, did support Cruz's call for a strict screening process for refugees entering the country in an effort to prevent an attack similar to the one in Paris.

"Everybody should go through the same screening process, but I can tell you that a persecuted Christian — a Christian family that has been uprooted in their community, whether it's in Iraq or Syria ... they're not Islamic terrorists," Bush told reporters in New Hampshire.

Democratic front-runner Hillary Rodham Clinton took to Twitter Friday and challenged all Republican candidates to disavow Trump's comments.

"This is shocking rhetoric," she wrote. "It should be denounced by all seeking to lead this country."

The Associated Press contributed to this report.

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