Brewer came to welcome the president to the state. Obama gave her a critique on her recently published book, "Scorpions for Breakfast."
"I felt a little bit threatened - if you will - in the attitude that he had," Brewer said. "He changed the subject to my book, and I asked him, 'Did you read my book?' and he said, 'I read excerpts,' and then he started down his dialogue of what he felt."
The feud has gone on since the Republican governor signed a controversial bill cracking down on illegal immigration in 2010.
Brewer's recently released book seems to have inflamed the situation.
The president, who was in town as part of a three-day, five-state tour following his State of the Union address, said Brewer's account of White House meeting between the duo two years ago was off the mark.
In a statement, the White House said "The president said he'd be glad to meet with her again, but did note that after their last meeting, a cordial discussion in the oval office, the governor inaccurately described the meeting in her book."
In the book, Brewer describes the president at lecturing her about immigration.
President Obama opposes the Arizona immigration law, calling it misguided.