WASHINGTON — The Justice Department rejected a last-ditch appeal from defense lawyers for the former F.B.I. deputy director Andrew G. McCabe, people familiar with the matter said on Thursday, as prosecutors have appeared close to charging him in a criminal case.

Lawyers for Mr. McCabe, who is being investigated over whether he lied to internal investigators about dealings with the news media, had argued that prosecutors lacked evidence to charge him. The lawyers detailed their position to top officials including Jeffrey A. Rosen, the deputy attorney general, who ultimately rejected their view. His deputy, Edward O’Callaghan, who was also present during the discussion, notified Mr. McCabe’s lawyers of the decision, one of the people said.

The case is politically fraught for the Justice Department because of President Trump’s repeated attacks on Mr. McCabe, who was the acting director of the F.B.I. when investigators opened the inquiry into whether the president obstructed justice. Charging Mr. McCabe would undoubtedly please Mr. Trump, but passing on charges could provoke his public displeasure.