"That was an error, if I said that," Brewer said about beheadings occurring in Arizona.
The Republican incumbent's June comments about beheadings were raised during a Wednesday debate by Democratic challenger Terry Goddard, who said the comments were false and damaging to Arizona's image.
Brewer didn't respond to Goddard's challenge about the beheadings claim - she instead changed the subject. Afterward, when reporters asked about the claim, she cut short the question-and-answer session.
But she since is acknowledging in interviews with The Associated Press and other media organizations that she was wrong.
She said she was referring to beheadings and other cartel-related violence in Mexico that she said could spill over into the United States and that she is sorry if people were misled.
"I misspoke, but you know, let me be clear, I am concerned about the border region because it continues to be reported in Mexico that there's a lot of violence going on and we don't want that going into Arizona."
Brewer apparently first referred to beheadings during a June 16 interview with FOX News' Greta Van Susteren, talking about "the kidnappings and the extortion and the beheadings and the fact that people can't feel safe in their community" in discussing controversy surrounding the immigration law.
She went further in a June 27 interview on Phoenix television station KPNX when asked about the beheadings claim.
"Oh, our law enforcement agencies have found bodies in the desert, either buried or just lying out there, that have been beheaded," Brewer said.