Venezuela is funding the illegal immigrant caravan, Vice President Mike Pence said Tuesday, backing up President Trump’s claims that there are bad elements within the thousands of people.

Mr. Trump said he doesn’t have specific proof to back up his claim a day earlier that Middle Easterners are part of the caravan, but said there “could very well be.”

The president also said he’s become good at estimating crowds, and figures there are 10,000 people coming as part of the caravan.

“Something needs to be done,” he said. “You can’t have this happen.”

He again threatened to deploy the U.S. military to secure the border.

On Monday Mr. Trump had said on Twitter that “criminals and unknown Middle Easterners are mixed in” to the caravan.

Reporters interpreted that to mean “terrorists,” and demanded proof that such persons were in the caravan, which Central American officials said is chiefly Hondurans.

The White House defended the president’s comments, pointing to Homeland Security figures about the number of people on terror watch lists denied entry to the U.S. — an average of seven a day in 2017.

But almost all of those came through airports. Fewer than one a day came through land borders, according to the government figures.

Mr. Trump said he has “very good information” about those in the caravan, and said given the overall migration trends, there are bound to be Middle Easterners amid the numbers.

Mr. Pence, standing with Mr. Trump in the Oval Office, reported he’d spoken earlier in the day with the Honduran president, who’d told him the caravan was organized by “leftist groups” and funded by Venezuela, a country deeply at odds with the administration.

“I’m not letting them in. They’re not coming in,” Mr. Trump said.

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