PHOENIX -- A day after the most contentious provision of Arizona's immigration law took effect, rallies were planned around Phoenix to protest the law that civil rights activists contend will lead to systematic racial profiling.

Leticia Ramirez has been telling immigrants who are in the United States illegally, like herself, that they should offer only their name and date of birth -- and carry no documents that show where they were born, if pulled over by police.

"We want to teach the community how to defend themselves, how to answer to police, how to be prepared, and to have confidence that they're going to have help," said Ramirez, a 27-year-old from Torreon in the Mexican state of Coahuila.

U.S. District Judge Susan Bolton ruled Tuesday that police can immediately start enforcing the law's so-called "show me your papers" provision. It requires officers, while enforcing other laws, to question the immigration status of those suspected of being in the country illegally.

The U.S. Supreme Court upheld the provision in June on the grounds that it doesn't conflict with federal law. Opponents argued that it would lead to systematic racial profiling and unreasonably long detention of Latinos, and unsuccessfully asked Bolton to block it.

Bolton said the law's opponents were merely speculating on racial profiling claims. She did leave the door open to challenges if the claims can be proven.

The 9th U.S. Circuit Court of Appeals is considering a request to halt the questioning requirement.

Immigration and Customs Enforcement, the federal agency that verifies people's immigration status for local officers, said the volume of calls it has received from local authorities for immigration checks and assistance hasn't increased from what it normally gets since the questioning requirement took effect.

In the meantime, a hotline by civil rights advocates has been fielding calls from people wanting to know their rights if questioned about their immigration status.

The advocates are asking people to document abuse and police departments not to enforce the provision as a way to gain cooperation from immigrants in reporting crimes. But not enforcing the provision could open up officers to lawsuits from people claiming authorities aren't complying with the law.

Advocates planned to gather Wednesday to address the Phoenix City Council about their concerns on the law and in front of the U.S. Immigrations and Custom Enforcement building to protest the law and federal immigration policies. A march to the Maricopa County jail in downtown Phoenix is scheduled for Saturday.

Arizona lawmakers passed the law in 2010 amid voter frustration with the state's role as the busiest illegal entry point in the country. Alabama, Georgia, Indiana, South Carolina and Utah have adopted variations on Arizona's law.

Republican Gov. Jan Brewer says it won't cure the state's immigration woes but could push the federal government to act on immigration reform.

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Fonseca reported from Flagstaff, Ariz.