Some of the demonstrators drove overnight to march 5 miles under a scorching sun in Phoenix, the Los Angeles Times said. Juan Baez, who became a U.S. citizen after entering the country illegally, came from San Diego with his wife, Guadalupe, their six children and his mother-in-law.
The entire family wore home-designed T-shirts reading: "We are hard workers, not criminals! We believe in USA justice. Arizona's SB 1070 is not justice."
Supporters of the law planned a counterdemonstration in the evening.
Gov. Jan Brewer stripped Attorney General Terry Goddard of any role in the court battle over the law, The New York Times reported. She acted after U.S. Justice Department lawyers met Friday with Goddard before holding a meeting with her.
The Obama administration openly opposes the Arizona law, which makes being an illegal immigrant a state crime. Goddard, a Democrat while Brewer is a Republican, also spoke out against the bill but said he is committed to doing his job in court.