WASHINGTON — Federal civil rights prosecutors have recommended charges against a New York police officer in the 2014 death of Eric Garner, three current and former officials said, but top Justice Department officials have expressed strong reservations about whether to move forward with a case they say may not be winnable.

Mr. Garner died on a Staten Island street after the police officer, Daniel Pantaleo, used a chokehold to subdue him. Officers had confronted Mr. Garner, who was unarmed, over accusations of selling untaxed cigarettes. His final gasps of “I can’t breathe,” captured on a cellphone video, became a rallying cry for protesters around the country.

In recent weeks, career prosecutors recommended civil rights charges against Officer Pantaleo and sought approval from the deputy attorney general, Rod J. Rosenstein, to seek an indictment, according to the officials. Mr. Rosenstein has convened several meetings that revealed divisions within the Justice Department over whether to move forward. No decision has been made, but one law enforcement official said that, based on the discussions so far, it appeared unlikely that Mr. Rosenstein would approve charges.

Attorney General Jeff Sessions has also been briefed on the case and could weigh in after Mr. Rosenstein makes his own recommendation, officials said.