(CNN) For days, as migrants have traveled thousands of miles toward the US-Mexico border, President Donald Trump has warned of the dangerous people who make up their pack.

He's tweeted that "[c]riminals and unknown Middle Easterners" are "mixed" in with the caravan, and, on Monday afternoon, doubled down on his claims, telling reporters on the South Lawn of the White House to "go into the middle" of the caravan and "search. You're gonna find MS-13. You're gonna find Middle Eastern."

While the President insinuates terrorists have infiltrated the group that CNN crews have observed to include mostly mothers and their children, a senior counterterrorism official has also refuted the President's claim.

"While we acknowledge there are vulnerabilities at both our northern and southern border, we do not see any evidence that ISIS or other Sunni terrorist groups are trying to infiltrate the southern US border," a senior counterterrorism official told CNN.

Officials at the Department of Homeland Security have been less direct, but have disproved the President's point nonetheless.

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