The proceedings came after a hearing earlier Thursday in Pennsylvania to discuss Mr Mangione's extradition back to New York where the shooting occurred. He appeared shackled in an orange jumpsuit, and afterwards was taken by plane to an airport on Long Island, New York, then by chopper to Manhattan.
Mr Mangione was arrested at a McDonald's in Altoona, Pennsylvania, five days after Mr Thompson, the UnitedHealthcare CEO, was shot and killed. He was found with a fake ID and so-called "ghost gun", police have said.
During the New York hearing on Thursday, Mr Mangione sat between his two lawyers - Karen Friedman Agnifilo, and her husband, Mark Agnifilo, who also is representing rapper Sean "Diddy Combs" in his sex trafficking case.
Mr Mangione nodded along during the hearing as New York Magistrate Judge Katherine Parker read him his rights, including the right to remain silent.
She also read the charges against him: two counts of stalking, a firearms offense, and murder through use of a firearm.
The proceedings were largely standard, but Mr Mangione's lawyer, Ms Agnifilo, who appeared in the courtroom on crutches, asked prosecutors to clarify how many cases Mr Mangione would face.
He already was indicted on state charges in New York, including first-degree murder in furtherance of terrorism, and now also faces federal charges.
Ms Agnifilo told the court that the overlapping cases - and a murder charge against Mangione that makes him eligible for the death penalty - were "confusing" and "highly unusual".
"I've never seen anything like what is happening here" in 30 years of practicing law, she said.
