The guidance has confused and angered immigration agents.

Mr. Moran, testifying to a Senate committee last week, said agents now have to go through a checklist when they encounter illegal immigrants. Those who give the right answers are likely to be released.

“The messaging on the training from CBP has been inconsistent at best,” he said.

Sen. Ron Johnson, Wisconsin Republican and chairman of the Homeland Security and Governmental Affairs Committee, said it sounded as though immigrants only had to say “magic words” to avoid arrest.

During the border surge this summer, Mr. Moran said, agents discovered that some of the illegal crossers had written scripts with them to coach them on what to say to be released into the U.S.

A Homeland Security spokeswoman said the hotline memo was intended to make sure stakeholders knew where to go for information.

“This provides one place for all stakeholders to find out more about the new DHS guidelines, deferred action, eligibility for new initiatives, or to register comment or complaint,” said Ginette Magana, the spokeswoman. “DHS continuously engages with stakeholders, members of Congress and interested individuals to provide the most up-to-date information and answer questions about any new initiatives.”

But the memos go further. The page providing the complaint hotline for Customs and Border Protection, which oversees the Border Patrol, specifically invites complaints from immigrants who believe agents didn’t follow Mr. Obama’s priorities.

“The CBP Info Center (CIC) is a toll-free service for individuals with questions about CBP procedures or who wish to register a complaint about an encounter with CBP that they believe to be contrary to guidance,” the department says on the CBP page.

The CBP page says it has only “limited assistance” available in Spanish for those calling to complain, but the complaint hotline for ICE specifically says it can handle calls both Spanish and English.

Homeland Security has had complaint lines for some time, and Mr. Obama picked a fight with Congress over an advocacy office in ICE several years ago. Congress canceled funding for the job, so Mr. Obama changed the title but kept the same person doing the same work and argued that he met the letter of the law.