President Trump defended his tweeted claim that "unknown Middle Easterners" are part of a 7,000-person migrant caravan traveling through southern Mexico, but conceded Tuesday there was "no proof."

Trump said that it was a reasonable assumption that there were Middle Eastern participants.

"I have very good information," Trump told reporters in the Oval Office. "There is no proof of anything. There is no proof of anything, but they could very well be."

[Rep. Andy Biggs: Look at the caravan's actions, and you'll see their wicked intent]

Trump was joined in the Oval Office by Vice President Mike Pence, who said that he spoke with Honduran Juan Orlando Hernandez, who blamed the government of Venezuela for initiating the caravan that appeared to begin spontaneously.

"[Hernandez] told me that the caravan that is now making its way through Mexico headed for the southern border was organized by leftist organizations and financed by Venezuela," Pence said.

The Central American leader blamed Trump's socialist nemesis in Venezuela after Trump said Monday he would cut foreign aid to Honduras and other countries for failing to stop the convoy, which crossed Guatemala into Mexico.

Pence also defended Trump's claim of possible Middle Eastern terrorist infiltrators.

"The United States of America intervenes and prevents 10 terrorists or suspected terrorists from coming into our country every day. So it's — it's inconceivable that there would not be individuals from the Middle East as a part of this growing caravan," he said.

Trump said he believed it was possible that Middle Eastern terrorists were part of the caravan, which could take weeks to reach the U.S. border, because of reports from the U.S. Border Patrol about the apprehension of Middle Eastern suspects.

Even if there aren't Middle Easterners in the caravan, Trump said they are likely to be attempting to cross the border at some point.

"I think there is a very good chance, honestly, that you have people in there," he said. "I also think there is a very good chance over the course of a period of time you have — or they don't necessarily have to be in that group. 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."

Journalists accompanying the large caravan have been unable to confirm Middle Eastern participants. Many members of the procession say they are fleeing poverty, violence, and corruption in Central America.