Republican Presidential candidate Ted Cruz has said the United States should refuse to accept any Muslim refugees from Syria but allow in Christians, explaining that "there is no meaningful risk of Christians committing acts of terror."

"If there were a group of radical Christians pledging to murder anyone who had a different religious view than they, we would have a different national security situation," the Texas Senator said at an event in South Carolina on Sunday, CBS News reports.

"We can't roll the dice with the safety of Americans and bring in people for whom there is an unacceptable risk that they could be jihadists coming here to kill Americans," he said, explaining that those in the Obama administration "pretend there is no religious aspect to this."

Cruz is among a number of Republicans who have expressed opposition to accepting migrants after one of the jihadists in the Paris attacks was revealed to have entered Europe with Syrian refugees coming through Greece.

Thus far, more than a dozen US states have said that Syrian refugees are no longer welcome due to security fears, including Michigan, Alabama, Texas and several other states. As reported by the Gospel Herald, the United States had promised to take about 10,000 Syrian refugees in the next 12 months.

Former Florida Gov. Jeb Bush similarly argued in favor of preferential treatment for Christian refugees from Syria during an interview on "CBS This Morning" Monday.

"But I do think there is a special important need to make sure that Christians from Syria are being protected because they are being slaughtered in the country and but for us who? Who would take care of the number of Christians that right now are completely displaced?" he said.

In turn, President Obama slammed suggestions from some Republicans that the White House should give Christians preference over Muslims during a speech given at the G20 summit in Turkey on Monday.  

"That's not American, it's not who we are," Obama said, urging America's politicians to fight the "dark impulse" to judge people for their beliefs.

"When I hear folks say that, well, maybe we should just admit the Christians but not the Muslims, when I hear political leaders suggesting that there would be a religious test for which person who's fleeing from a war-torn country is admitted, when some of those folks themselves come from families who benefited from protection when they were fleeing political persecution, that's shameful," the President added.

Meanwhile, US House Speaker Paul Ryan told reporters Tuesday morning that the Syrian refugee situation "requires a pause" and said that the ultimate solution is a strategy to defeat ISIS.

"ISIS showed they are committing an act of war against the West," he said, explaining that Republican party leaders had assembled a task force to consider legislation "as quickly as possible" that would suspend the admittance of Syrian refugees.

"This is a moment where it is better to be safe than sorry. So we think the prudent, the responsible thing is to take a pause in this particular aspect of this refugee program in order to verify that terrorists are not trying to infiltrate the refugee population," he added.