As expected, Anderson appointed noted defense attorney Judy Clarke of San Diego as Loughner's attorney.
Clarke waived a detention hearing and Anderson, on the recommendation of Assistant U.S. Attorney Wallace Kleindienst, remanded Loughner to detention pending a Jan. 24 hearing.
Clarke also demanded that the U.S. Attorney's Office in Phoenix be conflicted out of the case.
"There is great concern with proceeding any further than today with Arizona judges," Clarke said.
As the hearing ended, Anderson turned to the defendant and said: "Good luck to you, Mr. Loughner. We are adjourned."
The motive for the killing remains unknown. Loughner has not been cooperating with investigators, authorities said.
Official sources familiar with the investigation said local authorities are looking at a possible connection between Loughner and the American Renaissance, an online group known for its anti- government rhetoric.
The group is reportedly connected to the white supremacist New Century Foundation.