The American Civil Liberties Union, the Mexican American Legal Defense and Educational Fund and the National Association for the Advancement of Colored People were among groups that filed the latest challenge.
They filed the case in U.S. District Court on behalf of plaintiffs that include labor unions, a Tucson church, social-service organizations and numerous individuals.
The new suit, the fifth legal challenge filed since Gov. Jan Brewer signed the legislation, asks a federal judge to declare the measure unconstitutional and block it from taking effect in late July. The cases could be consolidated, and no court hearings have been scheduled.
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Key provisions of the law include requiring police enforcing other laws to verify a person's immigration status if there's "reasonable suspicion" of illegal presence in the United States. It also makes being in the country illegally a state crime and prohibits seeking day-labor work at roadside.
The lawsuit alleges that the law is unconstitutional because the federal government has responsibility to regulate immigration, and because enforcement of the law will violate protections for due process and equal treatment under the law.
The suit argues that enforcing the law will subject U.S. citizens and others to racial profiling and other harassment, interfere with delivery of social services, and deter people from approaching law enforcement to report crimes.
"This law is shameful and un-American and will undermine public safety," said Lucas Guttentag, director of the ACLU Immigrants' Rights Project.
County attorneys and sheriffs in Arizona's 15 counties were named as defendants.
The Maricopa County attorney's office declined to comment on the lawsuit. In Tucson, Pima County lawyers were studying the law and County Attorney Barbara LaWall has not made a decision on the law's constitutionality and a possible defense, Chief Deputy Amelia Cramer said.
The office of Attorney General Terry Goddard, who is responsible for defending state laws from legal challenges, was also studying the case and had not made any decisions, spokeswoman Molly Edwards said.
Brewer, who signed the legislation into law on April 23 and follow-up legislation one week later, expects that the lawsuits will be consolidated and her views "will be well represented," spokesman Paul Senseman said.
The law prohibits racial profiling, is constitutional and will be upheld, Senseman said.
Brewer has said that the federal government has failed to close the border to illegal crossings, and that requires state action. Other supporters of the law have argued that it will prompt illegal immigrants to leave the state on their own.
Arizona is the nation's busiest gateway for illegal border crossings, and the federal government has estimated that 460,000 illegal immigrants live in the state.
The four earlier lawsuits contain similar arguments as the new challenge. Those lawsuits were filed on behalf of individuals, including Phoenix and Tucson police officers, and a group representing Latino clergy.
At least three Arizona cities - Flagstaff, Tucson and San Luis - have authorized a legal challenge to the law but have not filed a lawsuit.
Federal courts upheld a 2007 Arizona law that allows the state to impose licensing sanctions against employers who knowingly employ illegal immigrants. The rulings rejected a challenge's argument that the state's authority was pre-empted by federal authority over immigration.
But the new law "is a greater and more explicit intrusion into the regulation of immigration," said Linton Joaquin, general counsel of the National Immigration Law Center, another group supporting the challenge. "It leads to the racial profiling that is inevitable."
Citing a provision that requires legal immigrants to have documents on their immigration status, supporters of the state law say it mirrors federal law.
However, the new state crimes and the requirement for police questioning are inconsistent with federal law, said Nina Perales, an attorney for the Mexican American Legal Defense and Educational Fund.
The Washington, D.C.-based American Center for Law and Justice said it would file a court brief to help defend Arizona's law.
Immigration is part of America, "but immigration must be lawful, and the Arizona law is clearly designed to protect and secure its borders without putting at risk the constitutional protections afforded to American citizens," said chief counsel Jay Sekulow.