The initial charges concern illegal possession of weapons and presenting false identification documents to the police.
The man was arrested in Pennsylvania, but prosecutors in the state of New York want him extradited there, and prosecutors in Manhattan, New York, are bringing forward five charges, including murder.
The 26-year-old did not object to being extradited, but his lawyer demanded a court hearing on the extradition, which is delaying the process.
States in the USA have different legal systems, which means that a formal extradition must take place so that the suspect is tried in the state where the crime was committed.
Shouted to reporters
The accused was led into the courtroom in Pennsylvania in orange prison clothes. At the entrance, he turned around and shouted a message to reporters about "insulting the intelligence of the American people", before being firmly led into the courtroom.
The judge decided that the suspect would not be released on bail.
The suspect was discovered by chance, according to court documents. An employee at McDonald's in Altoonia, Pennsylvania, noticed that he resembled the suspected shooter, whose pictures the police had released, and alerted them.
"Started shaking"
When one of the police officers who arrested him asked if he had recently been in New York, the 26-year-old is said to have "become silent and started shaking".
His backpack was then searched, and among other things, a pistol and silencer, both of which were allegedly manufactured using 3D printers, were found.
The CEO of the American insurance company United Healthcare, Brian Thompson, was shot multiple times early on Wednesday morning outside a hotel on Manhattan.
