Federal prosecutors in Manhattan have charged the suspect in the fatal shooting of UnitedHealthcare’s chief executive with four counts, including a charge of murder through the use of a firearm, a new complaint shows.

Other charges include two stalking counts and a firearms offense.

The federal charges come a day after the office of the Manhattan district attorney filed state murder charges against the suspect, Luigi Mangione, 26, in the killing of the executive, Brian Thompson. Mr. Thompson, 50, was gunned down on a Manhattan sidewalk this month.

The highest penalty Mr. Mangione could face if convicted in state court would be life in prison without parole. A spokeswoman for the district attorney, Alvin L. Bragg, said on Wednesday that the state case would proceed in parallel with any federal prosecution.

The new charges came just over two weeks after the predawn killing of Mr. Thompson on Dec. 4.

Surveillance footage showed a gunman approaching Mr. Thompson from behind outside a Hilton hotel in Midtown Manhattan, lifting a handgun fitted with a suppressor and firing at him several times before fleeing.

The authorities have said the suspect then fled uptown on an e-bike and soon left New York.

Mr. Mangione was arrested days later in a McDonald’s in Altoona, Pa., as he was eating hash browns and looking at his laptop. A fellow customer had told a friend that he resembled the person in photos that the police had shared widely, and an employee, overhearing the conversation, called the police.

This is a developing story and will be updated.