The document, written in 2002 by the Justice Department’s Office of Legal Counsel, concluded that state police officers have “inherent power” to arrest undocumented immigrants for violating federal law. It was issued by Jay S. Bybee, who also helped write controversial memos from the same era that sanctioned harsh interrogation of terrorism suspects.

The author of the Arizona law — which has drawn strong opposition from top Obama administration officials — has cited the authority granted in the 2002 memo as a basis for the legislation. The Obama administration has not withdrawn the memo, and some backers of the Arizona law said Monday that because it remains in place, a Justice Department lawsuit against Arizona would be awkward at best.

“The Justice Department’s official position as of now is that local law enforcement has the inherent authority to enforce federal immigration law,” said Robert Driscoll, a former Justice Department Civil Rights Division official in the George W. Bush administration who represents an Arizona sheriff known for aggressive immigration enforcement. “How can you blame someone for exercising authority that the department says they have?”