Top Homeland Security official: ISIS hasn't crossed border into U.S.

"Let's not unduly create fear and anxiety in the public by passing on speculation and rumor," Johnson said Wednesday on CNN's "Situation Room."

Hunter, a California Republican, claimed on Fox News on Tuesday night that he'd learned from Border Patrol officers that at least 10 ISIS fighters had been caught trying to cross the Mexican border -- and that "you know there's going to be dozens more that did not get caught by the Border Patrol."

Johnson said those claims aren't supported by "credible, specific intelligence to that effect." He said public officials should "be responsible in what we decide to share with the American public, so that the public is informed."

His comments came after a Homeland Security spokeswoman called Hunter's statement "categorically false."

"I look at the intelligence reports from overseas, from our southern border, from our intelligence community virtually every day, numerous times a day, to be on the lookout for something of that nature," Johnson said.

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"So what I would say to the American public is, we're vigilant in looking out for individuals of suspicion that may be crossing our border, and we have no specific intelligence that ISIL is planning to come into the U.S. through our southern border," he said, using another acronym for ISIS.

Hunter spokesman Joe Kasper said the congressman stands by his comments.

"A high level source informed the congressman -- it was also said that DHS is actively discouraging any talk of IS on the border," Kasper said.

"The congressman was conveying what he knows -- and what he was told," he said. "And as for DHS' statement, it makes sense that the left hand of DHS doesn't know what the right hand is doing -- it's been that way for a long time and we don't expect that to change. No surprise there."