President Donald Trump on Tuesday admitted he had “no proof” that “unknown Middle Easterners” were attempting to enter the United States as part of a migrant caravan moving towards the southern border, but alluded that such evidence was immaterial because “they very well could be.”

“I have very good information,” the president told reporters in the Oval Office after he was asked about a growing migrant caravan of more than 7,000 people moving toward the border with Mexico. Trump has slammed the movement in recent days and threatened to militarize the region amid his own baseless claims that “criminals” were among the group.

When pressed repeatedly by CNN’s Jim Acosta on Tuesday if he had any proof that people from the Middle East had joined the caravan, Trump later admitted: “There’s no proof of anything. There’s no proof of anything, but there very well could be.”

“I’m not letting them in,” the president later added. “They’re not coming in. We’re going to do whatever we have to, they’re not coming in.”

Sadly, it looks like Mexico’s Police and Military are unable to stop the Caravan heading to the Southern Border of the United States. Criminals and unknown Middle Easterners are mixed in. I have alerted Border Patrol and Military that this is a National Emergy. Must change laws! — Donald J. Trump (@realDonaldTrump) October 22, 2018

According to reporters traveling with the caravan, many people are migrants fleeing poverty and violence in Central America, set on making their way to the United States where they hope to apply for asylum. The caravan can offer those seeking refuge a relatively safe means of passage, according to The Washington Post.

“These people are fleeing from the poverty of their countries,” José Luis Laparra Calderón, the mayor of Huixtla, Mexico, told The New York Times. “These are working people. They aren’t bringing bombs. They want to improve their lives.”

The event has become an unexpected hot-button issue ahead of next month’s midterm elections as the White House has ramped up its attacks on Democrats’ immigration policy. Many have accused Trump of fear-mongering for political gain and pointed to the president’s past attacks on foreign citizens.

Vice President Mike Pence cited false statistics while standing next to Trump on Tuesday, saying that law enforcement apprehended “more than 10 terrorists or suspected terrorists per day at our southern border from countries that are referred to in the lexicon as ‘other than Mexico’ ― that means from the Middle East region.”

As HuffPost’s Elise Foley notes, that account is grossly misleading and represents all known or suspected terrorists that are stopped from coming to the U.S. by any means ― often on air travel ― from any country, not just from the Middle East and not just along the southern border.

Despite his lack of evidence, Trump doubled down on his claims, saying there was “a very good chance” such individuals were now part of the caravan.

“They don’t necessarily have to be in that group,” he said. “But certainly you have people coming up through the southern border, from the Middle East and other places that are not appropriate for our country. And I’m not letting them in.”

A spokesman for the Department of Homeland Security said late Tuesday that there were citizens from the Middle East and other regions in the caravan, and said some were “gang members or have significant criminal histories.” It’s unclear how many people DHS had identified, and the agency did not provide any statistics to back up the assertion.

.@DHSgov can confirm that there are individuals within the caravan who are gang members or have significant criminal histories. — Tyler Q. Houlton (@SpoxDHS) October 23, 2018