The Defense Department on Friday pushed back against Texas Gov. Rick Perry Rick PerryOVERNIGHT ENERGY: Democrats push resolution to battle climate change, sluggish economy and racial injustice | Senators reach compromise on greenhouse gas amendment stalling energy bill | Trump courts Florida voters with offshore drilling moratorium OVERNIGHT ENERGY: Trump signs major conservation bill into law | Senate votes to confirm Energy's No. 2 official | Trump Jr. expresses opposition to Pebble Mine project Senate votes to confirm Energy's No. 2 official MORE’s (R) claim that fighters from the Islamic State in Iraq and Syria (ISIS) might have entered the United States across its southern border.

Perry, who is weighing another run for the president in 2016, made the assertion Thursday during a speech at the conservative Heritage Foundation.

"There's the obvious great concern that, because of the condition of the border from the standpoint of it not being secure, and us not knowing who is penetrating across, that individuals from ISIS or other terrorist states could be [crossing]," he said. "There's a very real possibility that they may have already used that [strategy]."

But the Pentagon’s top spokesman, Rear Adm. John Kirby, shot down that allegation.

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“I've seen no indication that they are coming across the border with Mexico. We have no information that leads us to believe that,” he said on CNN’s "New Day."

Kirby said Pentagon leaders know the terrorist group does have “aspirations to hit western targets” and that the threat is something “we’ve got to take seriously, and we have to be ready for it.”

He added that the Pentagon doesn’t have a “hard and fast number” of how many foreign fighters are among the group’s ranks.

He pointed out that officials in the United Kingdom are trying to uncover the identity of a man with a British accent who appeared in the video showing the execution of American journalist James Foley.

Australian leaders also raised the issue of their citizens becoming radicalized and joining ISIS with Defense Secretary Chuck Hagel, when he visited the country earlier this month, Kirby added.

“It's a problem in many countries, and we face that problem here in America. It's just hard to get our hands around it,” Kirby said.