Texas Sen. John Cornyn (R) on Thursday warned his colleagues in the Senate that people who were "wearing some form of turban" were illegally immigrating into the United States by crossing the Southern border.

During a Senate Judiciary Committee hearing to consider amendments to the bipartisan immigration reform bill, Cornyn asserted that he had "anecdotal" evidence that only 25 percent of undocumented immigrants crossing the border were caught by U.S. Customs and Border Protection.

"In fact, anecdotally, the border patrol last -- on Sunday and Monday were telling me, they think they maybe catch one out of every four people coming across the border," he declared. "Maybe one out of every three. And that's a problem."

The Texas senator argued that this made the case for an amendment offered by Sen. Chuck Grassley (R-IA), which establishes "triggers" that prohibits legalizing undocumented immigrants until the Department of Homeland Security has established "effective control" of the border for six months.

Sen. Chuck Schumer (D-NY), however, pointed out that a 2012 Government Accountability Office (GAO) report found that the Border Patrol had a 82 percent effectiveness rate at catching illegal border crossings.

"I would love to see that report because I don't believe that's the case," Cornyn replied. "The problem is the effectiveness rate you referred to doesn't take into account the people that cross illegally and the department is not tracking. In other words, it doesn't take into account the people that get away, which could, according to the anecdotal reports, be two out of every three, three out of every four."

Cornyn added that he had also been told during his recent visit to the southern border in Texas that "we're not just seeing the border penetrated by people from Mexico or Central America."

"The rescue beacons are in English, Spanish and Chinese. And I said, 'Why Chinese?' And they said, 'Well, for $30,000, you can get one of the smugglers to get you up through Central America, through Mexico and into the United States.'"

He continued: "Another deputy sheriff in Brooks County showed me a picture of three gentlemen that they detained all wearing -- happened to be wearing some form of turban. And I said, 'Where are these folks from?' And they said, 'Afghanistan.' And as we all know, the border patrol had documented that people from countries of special interest including state sponsors of terrorism have been detained coming across the Southern border."

Earlier this year, Cornyn was criticized after he tweeted that a "friend" told him that 300 people were coming across the border onto his property "every night."

Watch this video from the Senate Judiciary Committee, broadcast May 9, 2013.