The man accused of gunning down a health insurance executive in a brazen hit in New York pleaded not guilty Monday to state charges including "terrorist" murder.

Luigi Mangione who wore a white shirt, and a burgundy sweatshirt, was shackled during his appearance in a Manhattan court where he was flanked by police officers, an AFP correspondent saw.

The suspect is charged in both state and federal court in the December 4 shooting of UnitedHealthcare chief executive Brian Thompson.

Monday's hearing came after Mangione, 26, appeared in a New York court last week to face federal charges also including murder following his dramatic extradition by plane and helicopter from Pennsylvania, where he was arrested at a McDonald's restaurant.

Thompson's murder brought to the surface deep public frustration with the lucrative US commercial healthcare system, with many social media users painting Mangione as a hero.

If convicted in the state case, Mangione could face life imprisonment with no parole. In the federal case, he could technically face the death penalty.

Mangioni's attorney Karen Friedman Agnifilo has sought clarity on how simultaneous federal and state charges would work, calling the situation "highly unusual."

Mangione was arrested in Altoona, Pennsylvania, on December 9 following a tip from staff at a McDonald's restaurant, after a days-long manhunt. 

He had travelled to New York by bus from Atlanta about 10 days before the crime, the Department of Justice said. After checking into a Manhattan hostel with false identification, he allegedly performed reconnaissance near the victim's hotel and the conference venue where the shooting took place.

Early on December 4, Mangione allegedly tracked Thompson, walked up behind him and fired several gunshots from a pistol with a silencer, the DOJ said. Afterward, he fled on a bicycle.