But Brewer, a Republican who became nationally known for her strong stand on illegal immigration, said she will remain active in politics, Capitol Media Services reported. She did not get specific about her plans.
"I'm not going away," she said. "I'm going to participate, I'm going to speak out on issues that I believe that are important."
Brewer said she also hopes to help elect "pragmatic" Republicans instead of "ideologues."
It is unclear if Brewer could have run again legally. Under Arizona law, governors are limited to two full terms or a full term and any part of another term.
Brewer, in an interview, said she believes she could seek another term. She was Arizona secretary of state in 2009 when President Obama named Gov. Janet Napolitano to his cabinet as secretary of homeland security. Brewer argues she was serving Napolitano's term not her own until she was elected governor in her own right in 2010.
"But there's a time to be, and a time to go," she said in opting not to push the issue. "It's the right time for me to move on."
In 2010, Brewer signed the Support Our Law Enforcement and Safe Neighborhoods Act, which gives police broad powers to question suspected illegal immigrants. She continues to make immigration a major issue.
Brewer also signed legislation repealing Napolitano's move to give the same-sex domestic partners of state employees the same benefits as spouses. But last month she vetoed legislation to allow businesses to refuse to serve customers on religious grounds, a law critics say is aimed primarily at homosexuals.
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