Alabama Gov. Robert Bentley, a Republican, did not offer specifics, but said that he has been told that many of the plots that have been foiled were being brought by people who came from refugee programs.
"I have been told by my law enforcement agency, by Homeland Security, that there have been some major threats against the United States after 9⁄11, and all of those individuals came out of refugee programs," Bentley said on CNN's "New Day" on Tuesday.
Pressed by CNN's Chris Cuomo, Bentley reiterated that was his understanding.
"Major threats that have occurred since 9⁄11, not necessarily all, but the major individuals that have been stopped, those individuals that have come out of refugee programs," Bentley said. "That's what I've been told. "
The State Department, Department of Justice, FBI and Department of Homeland Security did not immediately respond to requests for comment.
There are a few examples of threats carried about by refugees. The Boston Marathon bombers came to the U.S. as refugees from the conflict in Chechnya in 2002. In another case, two men from Kentucky who came to the U.S. as Iraqi refugees pleaded guilty to committing and supporting terrorism overseas.
On the other hand, the famously foiled shoe bomber was a British-born man.
But the authorities have charged at least 52 individuals in the U.S. in just 2015 with trying to support ISIS.
Kathleen Newland at the Migration Policy Institute think-tank told The Economist
that it's unlikely terrorists will try to use the refugee system to get into the country. Of 745,000 refugees resettled in the U.S. since Sept. 11, the publication said, only the two Iraqis from Kentucky have been arrested for terrorism.
Bentley said the decision on whether to allow in refugees has to be made on a case-by-case basis, but right now he feels that he has to protect the people of his state by refusing Syrian refugees.
He said that's the case even though many of them are children or youths and fleeing ISIS themselves.
"My heart says that we should let these people in simply because they are fighting ISIS and have been displaced by ISIS just like, you know, ISIS is our enemy also," Bentley said. "My head says that I have to protect the people of the state of Alabama and keep them secure."