(CNN) -- A labor union representing nearly 20,000 border patrol agents and staff Friday disputed comments made by Arizona Gov. Jan Brewer that most illegal immigrants coming across the southern border are smuggling drugs.

Brewer initially made the comments earlier this month during a debate of Republican gubernatorial candidates. She repeated them Friday when asked by a reporter for the basis of the claim.

"Well, we all know that the majority of the people that are coming to Arizona and trespassing are now becoming drug mules," Brewer said. "They're coming across our borders in huge numbers. The drug cartels have taken control of the immigration.

"So they are criminals. They're breaking the law when they are trespassing and they're criminals when they pack the marijuana and the drugs on their backs."

When pressed, Brewer explained that many are simply coming to the United States to look for work but "are accosted, and they become subjects of the drug cartels."

T.J. Bonner of the National Border Patrol Council told CNN that Brewer's claims were "clearly not the case." Bonner said that some undocumented immigrants caught by border patrol agents have drugs on them, and that they sometimes blame pressure from the drug cartels.

But, he said, those claims have little credibility because drug smugglers are typically transporting much larger quantities of drugs. And besides, he said, if what Brewer said were true, there would be many more prosecutions for drug smuggling.

Brewer's comments, Bonner said, don't "comport with reality -- that's the nicest way to put it."

Brewer doubled down on the comments later Friday, however, issuing a statement reiterating them.

"The simple truth is that the majority of human smuggling in our state is under the direction of the drug cartels, which are by definition smuggling drugs," Brewer's statement said, according to the Associated Press as reported in the Arizona Republic. "It is common knowledge that Mexican drug cartels have merged human smuggling with drug trafficking."

Brewer said the "human rights violations that have taken place (by the cartels) victimizing immigrants and their families are abhorrent."

Brewer's statement is the center of a controversy over a recently passed law that requires law enforcement officials to ascertain the citizenship of the subject of any investigation if they have reason to believe their suspect is in this country illegally. The U.S. Department of Justice is considering whether to file suit against the law.