"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," said Robert Bentley, governor of the southern US state.
"As your governor, I will not stand complicit to a policy that places the citizens of Alabama in harm's way," Bentley said in a statement on Sunday.
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"The acts of terror committed over the weekend are a tragic reminder to the world that evil exists and takes the form of terrorists who seek to destroy the basic freedoms we will always fight to preserve," the governor added.
"I will not place Alabamians at even the slightest possible risk of an attack on our people."
The governor of the midwestern US state of Michigan said on Sunday that he had decided to suspend arrivals of Syrian refugees under a program announced President Barack Obama.
"Given the terrible situation in Paris, I've directed that we put on hold our efforts to accept new refugees until the US Department of Homeland Security completes a full review of security clearances and procedures," Governor Rick Snyder said in a statement quoted in some US media on Sunday.
"There will be difficult days ahead for the people of France and they remain in our thoughts and prayers," said Snyder, whose state is home to one of America's largest concentration of inhabitants from the Middle East.
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"It's also important to remember that these attacks are the efforts of extremists and do not reflect the peaceful ways of people of Middle Eastern descent here and around the world," he added in his statement.
The leading newspaper in his state, the Detroit Free Press, reported that between 1,800 and 2,000 refugees have resettled in Michigan over the past year, about 200 of whom were from Syria.
Another US governor, Bobby Jindal of Louisiana, who also is running for the Republican party's 2016 presidential nomination, on Saturday sent a letter to President Barack Obama expressing "grave concern" about allowing Syrian migrants into the country, and saying it would be "prudent to pause the process."
"Authorities need to investigate what happened in Europe before this problem comes to the United States," Jindal wrote to Obama.
Jindal said Syrian refugees began arriving in New Orleans earlier this month, and said it is "irresponsible and severely disconcerting to place individuals, who may have ties to ISIS, in a state without the state's knowledge or involvement."
Friday's attacks in Paris that left at least 129 dead and hundreds injured have raised fears of a similar assault by Islamist extremists on US soil.
Obama announced in September that the United States would take in 10,000 Syrian refugees by September 2016.
Various Republican presidential hopefuls also insisted on Sunday that in the wake of the Paris attacks America must not take in Syrian refugees because they might include Islamic State militants.
But a White House aide said the plan to bring Syrian refugees into the country carries very little risk, because the vetting process is "robust" and the overall number of refugees relatively small.
"We cannot close our doors to these people," Ben Rhodes, Obama's deputy national security adviser told the Fox News Sunday program.
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