A judge in New York state has dismissed two terrorism charges against Luigi Mangione, the alleged killer of UnitedHealthcare CEO Brian Thompson.

However, Judge Gregory Carro during a hearing on Tuesday morning ruled a charge of second-degree murder against Mangione could stand.

He said prosecutors had failed to establish that there was enough evidence to justify the terrorism-related murder charges that they sought against Mangione.

Mangione is accused of gunning down Thompson on a busy Manhattan street in December last year.

In a written ruling, Carro stated that the allegations did not meet the definition of terrorism under state law.

Although prosecutors argued that writings left by Mangione demonstrated a terrorism motive, the judge noted that they failed to show that the suspect intended to exert political pressure on the government or terrorize the general population, which are key elements of New York's terrorism law.

There was no evidence presented that the defendant made any demands of the government or sought any particular governmental policy change, let alone that he did so by intimidation or coercion, Carro wrote.

The dismissed first-degree murder charge could have carried a maximum of life in prison without parole, while a conviction for the remaining second-degree murder charge could result in a minimum sentence of 15 to 25 years.

Mangione is also facing related charges of weapons possession and forgery, in addition to federal murder charges which could lead to the death penalty.

The judge denied the defense team's request to postpone the state trial until after the federal proceedings.

The trial hearings are set to start on December 1, with Mangione pleading not guilty to all charges.

Brian Thompson, a father of two and the head of UnitedHealth Group's insurance division, was fatally shot on December 4 while in New York City for a meeting. Mangione was arrested days later in Pennsylvania.

At the scene, police reported that Mangione had left a note criticizing the health industry and its perceived corruption.

Supporters of Mangione gathered outside court, holding signs proclaiming his innocence and urging for his release.