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“If there’s 11.5 million people here unlawfully in the country, you’re only going to get a small percentage each year, so you are in a way exercising prosecutorial discretion,” he said.

NumbersUSA, a group that pushes for stricter immigration limits, is funding the agents’ lawsuit.

Roy Beck, the group’s executive director, said that what’s at stake is ICE agents’ ability to deter more illegal immigrants, who could wreak havoc with the job market.

“Without immigration enforcement, the labor market would be filled until wages fell either to the global average or the federal minimum wage,” he said. “These agents are protecting every working American’s level of income and wages.”

In one instance raised in the complaint, ICE agent James D. Doebler arrested an illegal immigrant and tried to put him into deportation proceedings, even though his supervisors told him not to.

He now faces a three-day suspension — though he says he was just following a 1996 immigration law that requires him to begin deportation proceedings for anyone he catches who entered the country illegally.

Mr. Crane said agents face another dilemma: If they do follow orders and release someone who later goes on to commit a crime, they may open themselves up to a civil lawsuit.

Sen. Jeff Sessions, Alabama Republican, has written to ICE asking for an explanation of the Doebler case, and he said he is still waiting.

“The men and women who swore an oath to uphold the law and protect the public safety are now forced to ignore the law if they are to remain secure in their jobs,” he said.