(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.

When asked for evidence for the President's claim that "[c]riminals and unknown Middle Easterners are mixed in" with caravan migrants, a DHS official responded with a hodgepodge of numbers: "In FY 18, CBP apprehended 17,256 criminals, 1,019 gang members, and 3,028 special interest aliens from countries such as Bangladesh, Pakistan, Nigeria, and Somalia. Additionally, CBP prevented 10 known or suspected terrorists from traveling to or entering the United States every day in fiscal year 2017."

None of that, however, proves that criminals or people from the Middle East are in the caravan crowd. And on top of that, the countries the DHS official mentioned are actually South Asian and African, not in the Middle East.

There was also no mention of whether Customs and Border Protection made those apprehensions at the southwest border or elsewhere. It is also unclear how or where CBP prevented terrorists from traveling to the United States. CBP spokesperson Corry Schiermeyer said she would not comment on the President's tweets, and referred additional questions to DHS, which oversees CBP.

Former Homeland Security acting Undersecretary John Cohen told CNN that there has "clearly been an effort" by the administration to create a sense of fear as the caravan gets closer to the US.

"That fear, from a law enforcement perspective, is highly misplaced," Cohen said. "It may be effective at energizing the base, but it creates a needless fear of the caravan."

The President's tweets and comments come just about two weeks ahead of the 2018 midterm elections, where he is emphasizing immigration as a key issue. Trump has, without evidence, accused Democrats of allowing immigrants to overrun the borders.

The President has said, "Democrats want caravans. They like the caravans. A lot of people say, 'I wonder who started that caravan ...' " Trump has often returned to immigration as a talking point that will motivate his base voters to go to the polls in the midterms, and his policies on immigration have been cited as one of the key factors that led to his victory in 2016.

Right-wing news outlets had speculated about a terror-connection in the caravan in the days leading up to Trump's morning tweet.

On Fox News Sunday morning, Tom Fitton, a conservative legal advocate, cited remarks by the president of Guatemala, who said earlier this month at a conference in Washington, DC, that his country had arrested nearly 100 people "highly linked to terrorist groups, specifically ISIS."