The legislation requires law enforcement to demand immigration papers from anyone who they have a "reasonable suspicion" is in the country illegally.
She said she will not tolerate racial discrimination or profiling. Brewer also said she had worked with legislators to make sure the bill protects civil rights.
"We must enforce the law evenly and without regard to skin color, accent or social status," she said, adding that the bill's opponents are "over-reacting."
An estimated 1,200 protesters, many of them students, gathered outside the Capitol to demonstrate against the bill.
She urged the law's supporters and enforcers to be careful not to make "even the slightest misstep."
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