"But that's a luxury law enforcement can't afford," he said.
Jay Carney, White House press secretary, told CNN that President Barack Obama has been briefed on the threat.
Meanwhile, Nafis made an initial court appearance Wednesday at a federal courthouse in Brooklyn.
His attorney, a public defender, declined to comment.
Nafis was a student majoring in cybersecurity at Southeast Missouri State University from January to May of this year, said Ann Hayes, a spokeswoman for the university.