Luigi Mangione, the 26-year-old man charged with murder in the killing of UnitedHealthcare’s chief executive, pleaded not guilty on Monday as he was arraigned in New York State Supreme Court.

The Manhattan district attorney’s office has charged Mr. Mangione with first-degree murder, a terrorism-related offense, as well as two variations of second-degree murder and weapons charges. He faces the possibility of life in prison without parole.

Prosecutors said in court filings last week that Mr. Mangione’s actions were meant to further terrorism and were “intended to intimidate or coerce a civilian population” and to “affect the conduct of a unit of government by murder.”

Mr. Mangione also faces federal charges: The Southern District of New York charged him with murder through use of a firearm, which carries a maximum potential sentence of death, as well as two stalking counts and a firearms offense. He has pleaded not guilty to those charges as well.

The state case is expected to go to trial before the federal one, said Edward Y. Kim, the acting U.S. attorney for the Southern District, and state prosecutors said they would coordinate with federal agencies.

Mr. Mangione entered the courtroom for his arraignment on Monday wearing a maroon sweater and light-colored pants. His wrists and ankles were shackled. During the hearing, his lawyer, Karen Friedman Agnifilo, told the judge she was concerned about her client’s right to a fair trial. “His rights are being violated,” she said.