Mr Mangione is in jail in Pennsylvania, where he was formally charged with possession of an unlicensed firearm, forgery and providing false identification to police.
He was handcuffed at the wrists and ankles when he appeared in court there earlier on Monday.
Wearing jeans and a dark blue jersey, Mr Mangione seemed calm during the hearing, occasionally looking around at those present, including the media.
Last week’s shooting triggered a huge manhunt, with New York City investigators using one of the world’s largest digital surveillance systems as well as police dogs, drones and divers in a Central Park lake to search for the attacker.
Investigators revealed that finding Mr Mangione was a complete surprise, as they did not have his name on a list of suspects before Monday.
It was ultimately a McDonald’s customer in Altoona that recognised the suspect from media coverage and alerted an employee, who then tipped off the police.
When police arrived, Mr Mangione showed them a fake New Jersey driver’s licence with the name Mark Rosario, said court papers.
He “became quiet and started to shake” when an officer asked if he had been to New York recently, the criminal complaint adds.
When he was told he would be arrested if he lied about his name, he gave his real name, according to the court papers.
Asked why he lied, he told officers that “I clearly shouldn’t have”.
A search of his backpack uncovered a 3D-printed pistol, a 3D-printed silencer and a loaded magazine with six rounds of 9mm ammunition.
Prosecutors said he was also carrying a US passport and $10,000 cash, $2,000 of it in foreign currency, though Mr Mangione disputed the amount in court.