At a news conference at the state capitol just after 7:45 p.m. ET, Brewer said the bill "could result in unintended and negative consequences."
"I sincerely believe that Senate Bill 1062 could create more problems than it purports to solve," Brewer said.
The controversial bill sparked outcry from LGBT activists and drew vocal criticism from civic leaders, business interests and state economic groups.
Defenders of the measure said it was a key safeguard of religious freedom.
Major corporations came out strongly against the proposal. Apple, Inc., which recently announced plans to build a new manufacturing plant in Mesa, Az., was joined by American and Delta airlines, Marriot Hotels, Intel, PetSmart, Yelp, Major League Baseball and others in announcing their opposition to the bill.
The bill threw Arizona's stint as host of next year's Super Bowl into jeopardy, too. The NFL had been mulling moving the game from the Phoenix-area city of Glendale if the bill were signed into law, Sports Illustrated reported.
And several Republicans — from Sen. John McCain and Sen. Jeff Flake, both of Arizona, to former GOP presidential nominee Mitt Romney — urged her to veto the bill.
The Republican-controlled state legislature passed the measure last week.
The bill permitted any business, church or person to cite the law as a defense in any legal action brought by the government or individual claiming discrimination.
Proponents called the bill a slight adjustment to the state's existing freedom law, which does not grant protections to people based on sexual orientation. But the law would have trumped local ordinances that offer protections for LGBT individuals in places like Phoenix, Flagstaff and Tucson.
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