Luigi Mangione, 27, was arrested in December 2024 and charged with fatally shooting UnitedHealthcare CEO Brian Thompson on a sidewalk in Midtown Manhattan.
Public officials condemned the shocking assassination.
Mangione became a folk hero to some in the United States who decry steep healthcare costs.
He has pleaded not guilty to murder and other charges and is expected to face trial next year.
Mangione has pleaded not guilty in a separate federal case where prosecutors plan to seek the death penalty.
Mangione wore a grey suit and a white shirt with a red checkered pattern and said nothing as officers removed his handcuffs at the defence table.
Mangione's lawyers are seeking to block prosecutors from using evidence allegedly found in his backpack during his arrest and statements he made to police, arguing he was illegally searched and questioned.
Prosecutors called a security camera technician to testify about videos they played in court that appeared to show Mangione at a McDonald's restaurant in Pennsylvania, where he was arrested after being recognised from news photos.
Several supporters of Mangione appeared outside the courthouse before the hearing, including one dressed as the villain from the video game Super Mario Bros, bearing a sign that said, "When patients die, profits rise," and a woman with a "Free Luigi" sash.
The hearings before Judge Gregory Carro could last the week and feature testimony from witnesses involved in Mangione's arrest in Pennsylvania.
The defence lawyers are seeking to block prosecutors from presenting evidence police say was found in Mangione's backpack, including a 3D-printed gun, a silencer, electronic devices and journal writings that appear to implicate him in the killing.
Mangione's lawyers are also seeking to suppress statements he gave to police during his arrest, saying police did not give Mangione proper notice of his legal rights.
Prosecutors with the office of Manhattan District Attorney Alvin Bragg have opposed Mangione's requests to suppress the evidence and denied his claims that he was illegally searched and questioned.
Mangione could face life in prison if convicted of murder in the second degree, which is defined as an intentional killing.
He also faces seven counts of criminal possession of a weapon and one count of possessing a false identification.
Carro dismissed two terrorism counts against Mangione in September, concluding prosecutors had not presented enough evidence that Mangione intended to intimidate health insurance workers or influence government policy.
Trial dates have not been set in either the state or federal cases.
Mangione has been held in federal custody in Brooklyn since his arrest.
