President Trump on Tuesday acknowledged that he has no proof that people of Middle Eastern descent have joined a large migrant caravan moving toward the U.S.-Mexico border, tempering a claim he has made in recent days.

“There’s no proof of anything. But there could very well be,” Trump said in remarks in the Oval Office on Tuesday afternoon.

His remarks came after several administration officials, including Vice President Pence, sought to back up the president in the face of skepticism about his claim this week.

The president maintained that he has “very good information” from Border Patrol and other officials.

“They say it happens all the time from the Middle East,” Trump said.

Trump has faced criticism for suggesting it is problematic on its own that people from the Middle East might be part of the group of migrants and that they would therefore be terrorists. Asked about this in the Oval Office, Trump said Border Patrol officials have told him they have intercepted “all sorts of people” of Middle Eastern descent trying to enter the United States over the years.

“They’ve intercepted good ones and bad ones. They’ve intercepted wonderful people from the Middle East, and they’ve intercepted bad ones,” he said.

Trump first claimed in a tweet Monday that “Criminals and unknown Middle Easterners are mixed in” the caravan, which the president has pointed to repeatedly as he seeks to elevate immigration as an issue ahead of the Nov. 6 midterm elections.

When asked for evidence of his claim later Monday, Trump told a television reporter to “take your camera, go in the middle and search” the caravan, which originated in Honduras and includes mostly mothers and their children, based on what reporters have observed.

Asked while sitting for an interview at a Washington Post event Tuesday if he has evidence, Pence sought to back up his boss.

“It’s inconceivable that there are not people of Middle Eastern descent in a crowd of more than 7,000 people advancing toward our border,” the vice president said, asserting that “there are statistics on this.”

“In the last fiscal year, we 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,” Pence said.

He seemed to be referencing statistics shared by the Department of Homeland Security on Monday when asked by reporters for evidence to support Trump’s claim.

Those statistics, from fiscal 2017, were not specific to the U.S.-Mexico border and offer no proof that anyone in the current caravan is a Middle Easterner or terrorist.

DHS also told reporters Monday that Customs and Border Patrol agents had in fiscal 2018 “apprehended 17,256 criminals, 1,019 gang members, and 3,028 special interest aliens from countries such as Bangladesh, Pakistan, Nigeria, and Somalia.” None of the countries mentioned are in the Middle East.

In a statement after his remarks, a Pence spokeswoman made no mention of terrorists being stopped at the U.S.-Mexico border.

“In 2017 alone the U.S. apprehended on average between 10 suspected terrorists a day attempting to enter the country illegally,” said the spokeswoman, Alyssa Farah. “And those are just the ones we catch. It’s inconceivable that this caravan — which is being broadcast around the globe — hasn’t already been infiltrated with ties to extremism.”

A Department of Homeland Security spokesman tweeted Tuesday that the caravan includes people from all over the world.

“Citizens of countries outside Central America, including countries in the Middle East, Africa, South Asia, and elsewhere are currently traveling through Mexico toward the U.S.,” DHS spokesman Tyler Q. Houlton said in a tweet.

Houlton also tweeted that the department has confirmed that some migrants who are part of the caravan “are gang members or have significant criminal histories.”

Secretary of State Mike Pompeo also spoke about the caravan at a State Department news conference Tuesday evening, arguing that it presents a national security risk to the United States.

“There is no proper accounting of who these individuals in the caravan are,” Pompeo said, adding that the caravan “will not cross our southern border illegally under any circumstances.”

Pence spoke briefly about immigration during an appearance largely focused on the administration’s plans for a new branch of the military to be known as the Space Force. His interview was part of a larger program titled “Transformers: Space.”

During his remarks, Pence repeated Trump’s vow to stop the caravan before it reaches the U.S. border and blamed Democrats for the country’s immigration challenges.

“We’re going to do everything in our power to keep this caravan from coming north and violating our border,” Pence said.

In the Oval Office, Pence said that the president of Honduras told him that the caravan was organized by leftist groups and financed in part by Venezuela.

“And the Democrats? And the Democrats?” Trump asked, prompting laughter from those gathered in the office. The president has sought to tie the caravan to Democrats in his recent campaign trail remarks.

A moment later, when pressed by a reporter on the claim, he responded: “We’re going to find out about that.”