The law requires local and state law enforcement to question people about their immigration status if there's reason to suspect they're in the country illegally, and makes it a state crime to be in the United States illegally.
The follow-on bill signed by Brewer makes a number of changes that she said should lay to rest concerns of opponents.
``These new statements make it crystal clear and undeniable that racial profiling is illegal, and will not be tolerated in Arizona,'' she said in a statement.
Lawyers whose clients have filed lawsuits challenging the law did not immediately return calls for comment.
The changes include one strengthening restrictions against using race or ethnicity as the basis for questioning by police and inserts those same restrictions in other parts of the law.
Another change states that immigration-status questions would follow a law enforcement officer's stopping, detaining or arresting a person while enforcing another law. The earlier law had referred to a ``contact'' with police.
Another change specifies that possible violations of local civil ordinances can trigger questioning on immigration status.
Both the law and the changes to it will take effect July 29 unless blocked by a court or referendum filing.
Lawmakers approved the follow-on bill several hours before ending their 2010 session.
The sponsor, Sen. Russell Pearce, unveiled the changes at a House-Senate conference committee Thursday. He later said the revisions would not change how the law is implemented but provide clarifications on intent and to make the bill more defensible in court.
``There will be no profiling,'' Pearce, R-Mesa, said in an interview.
Pearce said the change from the ``contact'' wording doesn't require a formal arrest before questioning but helps make it clear that racial profiling is not allowed.
``You have to have a real legitimate reason based on some violation or some suspicious activity based on some legitimate reason. It cannot be just on how you look.''
There was little debate by lawmakers when the bill was considered, but Democrats opposed to the law criticized the new bill, too.
Rep. Ben Miranda, an attorney who is helping representing a group of Latino clergy who are behind one of three lawsuits filed Thursday to challenge the law, said the Republican-led Legislature's approach to illegal immigration is misguided.
``All parts of Arizona cry out for law enforcement that is reasonable and directed at the most serious crimes that we have in the community,'' the Phoenix Democrat said Thursday night. ``The racial profiling element is real.''
Rep. Kyrsten Sinema, D-Phoenix, said the new wording regarding local civil ordinances could spur complaints of racial profiling based on complaints about cars parked on lawns and debris in yards.
Organizers of two referendum campaigns challenging the original law have said they will adjust their filings to reflect new provisions added by the Legislature.
Filing of referendum petitions by July 29 would put implementation of the legislation on hold pending a vote. That vote would either be in November or in 2012, depending largely on when the petitions are filed.