Updated Wednesday at 1:43 p.m. ET

Last week's terrorist attacks in Paris and how the U.S. should respond to an influx of Syrian refugees are becoming flashpoints in political races.

The first test of how it could directly influence a contest could come this Saturday in the Louisiana governor's race. Trailing his Democratic opponent, John Bel Edwards, GOP Sen. David Vitter launched an ad that uses footage from Friday's deadly attacks in France.

"One of the France ISIS terrorists entered France posing as a Syrian refugee," an announcer in the ad says. "Now, Obama's sending Syrian refugees to Louisiana."

The video shows a letter from Vitter to Obama urging him to stop resettlement of the war-torn refugees in Louisiana, while, the ad alleges, Edwards sides with Obama.

Following the Paris attacks, Edwards wrote on Facebook he would work with federal authorities to "accommodate refugees." That post has since been edited, and Edwards later put out a statement that he supports a "pause" on allowing refugees in.

The Democratic Gumbo PAC, which is supporting Edwards, put out a counter ad Wednesday accusing Vitter of muddying Edwards' position, downplaying the threat to Syria and skipping Senate hearings on the issue.

Still, Vitter and Republicans hope the focus on the issue could help him swing some momentum his way in a race where he's been fending off personal attacks. A brutal Edwards ad earlier this month alleged that "Vitter chose prostitutes over patriots" — a reference to the 2007 D.C. Madam scandal in which Vitter was identified as a client. Edwards said Vitter skipped a vote to recognize soldiers who had died in favor of taking a call from the prostitution ring.

The issue is becoming a hot one in the presidential contest, too, with all of the GOP hopefuls each trying to show they are the best choice on national security.

Ohio Gov. John Kasich put out an online ad on Tuesday, accompanied by a fundraising plea to help air it, that highlights what he has said in the aftermath of the attacks and underscoring his own foreign policy experience.

"On-the-job training for president of the United States doesn't work," Kasich said. "We've done it for eight years — it does not work."

Kasich, who is trailing in the polls, said in a speech at the National Press Club Tuesday, though, that he wasn't aware of the ad, even though it was sent out by his own campaign.

"I didn't know they did that," he said, "and I don't know who did it, and I don't know what's behind it."

Kasich told NPR's Audie Cornish he also supports a "pause" in allowing Syrian refugees until they can be vetted — a reversal of his earlier support for resettlement.

Billionaire Donald Trump, who continues to lead Republican presidential polls, has radio ads in Iowa, New Hampshire and South Carolina in which he says, "The tragic attacks in Paris prove once again that America needs to get tough on radical Islamic terrorism."

He charges that Obama is "out of touch," has "no strategy" and is trying to bring in "hundreds of thousands of refugees" from Syria. Obama has announced that his administration would like to bring in 10,000, not hundreds of thousands.

Trump adds that he would "quickly and decisively bomb the hell out of ISIS."

In an aggressive Instagram video, Trump also says that the influx of refugees should be stopped. Despite Trump's lack of foreign policy experience, a Reuters poll out Tuesday showed him tied with Hillary Clinton as best to handle terrorism.

"We don't even know who they are!" he exclaimed. "They could be ISIS — they could be anybody. What is our president doing — is he insane?"

Ben Carson, who has been nipping at Trump's heels in the GOP race, has also spoken out on the issue, and a superPAC backing the neurosurgeon released an ad touting his hard-line opposition to allowing Syrian refugees into the U.S.

"When the president says things like, you know, through an executive order, 'I'm going to bring 100,000 people in here from Syria,' Congress needs to say, 'You do that, and we're going to defund everything, including your breakfast,' " Carson says in a clip used in the ad.

Carson, an outsider candidate with no prior political experience, has been fending off criticisms he is unable to grasp foreign policy — a claim magnified by a New York Times story that quoted an adviser saying, "Nobody has been able to sit down with him and have him get one iota of intelligent information about the Middle East."

Down ballot, Pennsylvania Sen. Pat Toomey's campaign manager sent out a fundraising email, based on his opposition to letting Syrian refugees into Pennsylvania.

"Senator Toomey believes nothing is more important than the security of the American people. To that end, he is pushing to suspend the admission of Syrian refugees into the United States until we are able to determine, with full confidence, that there are no security risks among them. ... If you agree with Senator Toomey, that nothing trumps the security of the American people, join the cause here."

The link brings supporters to a "contribute" page.

Copyright 2015 NPR. To see more, visit http://www.npr.org/.

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