President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE said there was "no proof of anything" Tuesday when pressed over his comments that people from the Middle East are among those traveling to the U.S. border in an migrant caravan that began in Central America.

Trump acknowledged during his comments at the White House that he has seen no evidence to support his assertion that the caravan includes people from the Middle East.

"There's no proof of anything," Trump said, while adding that "there very well could be."

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Trump did not shy away from his earlier declarations about the caravan, saying he had frequently spoken with people who work for the Border Patrol and that they had told him of intercepting Middle Eastern people passing through the southern border.

"They have intercepted many people from the Middle East," he said.

"They've intercepted good ones and bad ones. They have intercepted wonderful people for the Middle East. And they have intercepted bad ones."

Trump has been talking up the caravan, which is still roughy 1,000 miles from the U.S. border, for more than a week as he seeks to rev up the GOP base before the midterm elections on Nov. 6.

He was joined Tuesday by Vice President Pence, who earlier in the day had said it was "inconceivable" that some people from the Middle East wouldn't be in the caravan.

Pence doubled down on those remarks in the Oval Office, reiterating that “it is inconceivable that there would not be individuals from the Middle East as a part of this growing caravan.”

Pence also said that the president of Honduras told him that the caravan had "been organized by leftist groups in Honduras that were being financed, in part, by Venezuela."

The remarks seemed designed to play up the security implications of the caravan, though it is far from clear that there is much danger of anyone in the widely reported group being able to enter the United States.

Asked if he was using the caravan to stoke fear ahead of the midterms, Trump said: "I’m a very nonpolitical person, and that’s why I got elected president."