(CNN) -- Four groups that advocate for immigrant rights said Thursday they will challenge Arizona's new immigration law, which allows police to ask anyone for proof of legal U.S. residency.





The Mexican American Legal Defense and Educational Fund, the American Civil Liberties Union, the ACLU of Arizona and the National Immigration Law Center held a news conference Thursday in Phoenix to announce the legal challenge.





"The Arizona community can be assured that a vigorous and sophisticated legal challenge will be mounted, in advance of SB1070's implementation, seeking to prevent this unconstitutional and discriminatory law from ever taking effect," said Thomas A. Saenz, president of the Mexican American Legal Defense and Educational Fund, known as MALDEF.





"This law will only make the rampant racial profiling of Latinos that is already going on in Arizona much worse," said Alessandra Soler Meetze, executive director of the ACLU of Arizona. "If this law were implemented, citizens would effectively have to carry 'their papers' at all times to avoid arrest. It is a low point in modern America when a state law requires police to demand documents from people on the street."





Republican Arizona Gov. Jan Brewer signed the law last week. It goes into effect 90 days after the close of the legislative session, which has not been determined.





Brewer and others who support the law say it does not involve racial profiling or any other illegal acts.





"Racial profiling is illegal," Brewer said after signing the bill Friday. "It is illegal in America, and it's certainly illegal in Arizona."





The National Coalition Of Latino Clergy & Christian Leaders said Sunday it also planned legal action.





"Our churches and pastors in Arizona are outraged about the significant threat this anti-immigrant law will have in the lives of Arizona's Latinos," said the Rev. Miguel Rivera, the group's chairman.





"This policy violates the rights of American citizens, particularly the fast-growing Latino population of Arizona, by eliminating the basic right of due process, which we are certain that the courts will agree," Rivera said.





The law requires immigrants to carry their alien registration documents at all times and requires police to question people if there is reason to suspect they're in the United States illegally. The measure makes it a state crime to live or travel through Arizona illegally.





It also targets those who hire illegal immigrant day laborers or knowingly transport them.





In addition to signing the law, Brewer also issued an executive order that requires training for local officers on how to implement the law without engaging in racial profiling or discrimination.





"This training will include what does and does not constitute reasonable suspicion that a person is not legally present in the United States," she said.





Some officials in Arizona have expressed their displeasure with the measure. Phoenix Mayor Phil Gordon said Thursday that he is "very disappointed."





He said he is concerned that calls to boycott Arizona businesses and tourism will harm the state.





"I'm very incredulous that our state leaders -- our so-called leaders -- have allowed our state to be split when we're suffering economic hardships," Gordon told CNN.





Other critics say the bill is unconstitutional and will trample residents' civil rights.





"Quite simply, this law is a civil rights disaster and an insult to American values," said Mary Bauer, legal director of the Southern Poverty Law Center. "No one in our country should be required to produce their 'papers' or demand to prove their innocence. What kind of country are we becoming?"





But a national Republican leader said Thursday that Arizona is just filling a void left by the federal government.





"I think the people of Arizona have a right to pass their laws under the 10th Amendment," House Minority Leader John Boehner said. "I think it is clearly a result of the federal government's failure to secure our border and to enforce our laws."





Gordon said the real solution is comprehensive immigration reform that would allow more immigrants to legally enter the United States.





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