One day after winning a primary making him the GOP's Senate nominee in New Hampshire, Scott Brown said Islamic militants could already be crossing the border into the United States.

Brown also said that the U.S. shouldn't rule out putting ground troops in the Middle East to fight insurgents with the Islamic State in Iraq and Syria (ISIS).

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"As you know, what happened recently with the beheading of one of our own, there's deep concerns that there are members of ISIS actually coming through the border right now," Brown said on Fox News.

"We need to secure the border, once and for all," Brown said. "We need to make sure that we have an immigration policy that works. But not one that rewards that illegality with incentives. And the president needs to really rethink very, very, seriously what he's about to do.

"And does it mean boots on the ground?" he said. "Everything should be on the table. Of course, we don't want another world war. But to immediately take things off the table is wrong."

Texas Gov. Rick Perry (R) last month said "it's a very real possibility" that members of ISIS have crossed the border, but there's been no evidence so far to support the suggestions.

President Obama will deliver a prime-time address to the nation on Wednesday night, where he will outline his strategy for dealing with ISIS. It's possible Obama will announce he is expanding airstrikes against ISIS from Iraq to Syria. 

A number of lawmakers have said they would not want to see U.S. ground troops used to fight ISIS.