PHOENIX – An Arizona congressman urged the Obama administration on Sunday not to cooperate when illegal immigrants are picked up by local police if a tough new state immigration law survives legal challenges.

U.S. Rep. Raul Grijalva, a Democrat, and civil rights activists spoke to thousands of people gathered at the state Capitol and called on President Obama to fight the law, promising to march in the streets and invite arrest by refusing to comply.

“We’re going to overturn this unjust and racist law, and then we’re going to overturn the power structure that created this unjust, racist law,” Grijalva said.

Obama has called the new law “misguided” and instructed the Justice Department to examine it to see if it’s legal. It requires police to question people about their immigration status — including asking for identification — if they suspect someone is in the country illegally. Opponents say it would lead to racial profiling because officers would be more likely to ask people who look Hispanic.

Supporters have dismissed concerns about profiling, saying the law prohibits the use of race or nationality as the sole basis for an immigration check. Gov. Jan Brewer, who signed the measure Friday, has ordered state officials to develop a training course for officers to learn what constitutes reasonable suspicion someone is in the U.S. illegally.

State Sen. Russell Pearce, the Mesa Republican who sponsored the legislation, said it’s “pretty disappointing” that opponents would call on the federal government to refuse to cooperate with Arizona authorities.

“It’s outrageous that these people continue to support law breakers over law keepers,” Pearce said Sunday.

Protesters, some of whom came from as far away as Texas, clustered under trees for shelter from Arizona’s searing sun and temperatures that approached 90 degrees. Police said it was peaceful and there were no clashes.

Bill Baker, 60, took time off work at a downtown Phoenix restaurant to sell umbrellas and Mexican and American flags to the largely Hispanic crowd. He said he wasn’t making much money, but he wanted to help them exercise their freedom of expression — even though he supports the law they all showed up to oppose.

“If I go to another foreign country, if I go to Mexico, I have to have papers,” Baker said. “So I don’t feel there’s anything particularly harsh about the law.”

Arizona has an estimated 460,000 illegal immigrants.