Alabama Governor Robert Bentley on Sunday announced he will refuse Syrian refugees who are trying to relocate to Alabama.

"After full consideration of this weekend's attacks of terror on innocent citizens in Paris, I will oppose any attempt to relocate Syrian refugees to Alabama through the U.S. Refugee Admissions Program," Bentley said in a statement. "I will not stand complicit to a policy that places the citizens of Alabama in harm's way."

At this point, Alabama has one refugee processing center in the state approved by the State Department. It's in Mobile, and so far, no Syrian refugees have been relocated to Alabama.

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Alabama has also increased law enforcement presence at major events, although the governor's statement also said, " To date, there has been no credible intelligence of any terrorist threats in Alabama."

With the threat of extremist attacks looming over the United States, and recent suspicions that one of the Paris attackers may have entered France as a Syrian migrant, Republican presidential candidates have called for the United States to halt its Syrian refugee policy.

"Bringing people into this country from that area of the world I think is a huge mistake, because why wouldn't they infiltrate them with people who are ideologically opposed to us?" former neurosurgeon Ben Carson said in an interview on "Fox News Sunday."

Secretary of State John Kerry announced in September that the U.S. would increase the number of refugees it lets into the country, raising the total to 100,000 by the year 2017. The White House had previously said it would do a thorough background check before allowing them across the U.S. border.

But on Sunday, Florida Sen. Marco Rubio, another contender for the Republican presidential nomination, posed the problem of how to vet the refugees.

"We can't background check them," Rubio said on ABC News. "You can't pick up the phone and call Syria."

"That's one of the reasons why I said we won't be able to take more refugees," he added. "It's not that we don't want to; it's that we can't because there's no way to background check someone that's coming from Syria."

GOP Congressional leaders have voiced similar concerns: On Sunday, House Homeland Security Committee chairman Michael McCaul, R-Texas, told NBC News that the refugee crisis "causes a great concern on the part of policymakers, because we don't want to be complicit with a program that could bring potential terrorists into the United States."

But Ben Rhodes, the White House deputy national security adviser, is pushing back against the GOP insistence that the U.S. Syrian refugee policy must change.

Making the rounds on political talk shows Sunday morning, Rhodes affirmed that the country is still poised to take in migrants from the war-torn country.

"We're still planning to take in Syrian refugees," Rhodes said on Fox News Sunday. "We have very robust vetting procedures for those refugees. It involves our intelligence community, our National Counterterrorism Center, extensive interviews, vetting them against all information."

The White House official added, on CNN, that the concern of foreign fighters entering the country has been present "from the very beginning of this counter-ISIL campaign."

"We have made that a focus, so that we're working with countries to share information, to improve their laws and authorities to be able to monitor and detain people," Rhodes said, mentioning that the G-20 summit that President Obama is currently attending in Turkey will continue to focus on the threat.

On NBC News, Rhodes made a plea for empathy for those escaping the horrors of Syria's four-year-long war.

"We're also dealing with people who suffer the hardest of war -- women and children, orphans," he said. "We can't just shut our doors to those people. We need to sort out how to focus on that terrorists that we need to keep out of the country but I think we do need to do our part to take those refugees who are in need."