Jared Loughner, dressed in a tan detention uniform and shackled, appeared before U.S. Magistrate Lawrence Anderson, who appointed federal public defender Judy Clark as Loughner's attorney, The Arizona Republic reported.
Anderson ordered Loughner held without bond, the Arizona Daily Star reported.
Loughner is accused of opening fire at a political event Saturday in Tucson, killing six people and wounding 14 others, including Giffords, who was shot in the head. Among the dead were U.S. District Judge John Roll, presiding federal judge for Arizona, and Gabe Zimmerman, an aide to Giffords.
Federal officials charged Loughner, 22, with murder in the deaths of Roll and Zimmerman, and attempted murder in the wounding of Giffords and two of her staffers.
Clarke, who defended "Unabomber" Ted Kaczynski and helped in the case of Zacarias Moussaoui, a conspirator in the Sept. 11, 2001, terrorist bombings in the United States, waived a detention hearing and Anderson remanded Loughner to detention pending a Jan. 24 hearing.
CNN reported the defendant answered in the affirmative direct questions from Anderson about aspects of the hearing.
Federal judges from the Southern District of Arizona recused themselves from hearing the case because Roll was their colleague. Clarke asked Anderson to exclude the rest of the Arizona federal bench, too.
"There is great concern with proceeding any further than today with Arizona judges," Clarke said.
She also asked the U.S. attorney's office in Phoenix be excluded because of conflict of interest.
Anderson told Clarke she needed to file motions, the Republic said.
Loughner is expected to face a series of charges in state courts, officials told the Republic. Pima County Attorney Barbara LaWall said her office would file charges including murder, attempted murder and aggravated assault against Loughner after reviewing police reports.
Investigators said they haven't found a link between Loughner and extremist groups and he appears to have acted alone, The Washington Post reported.
Court documents indicated Loughner planned the shooting. In a safe at his parents' home -- where he lived -- investigators found an envelope with the words "I planned ahead" and "my assassination" written on it, along with the name "Giffords.'' Also in the safe, investigators found a letter to Loughner from Giffords in which she thanked him for attending a similar event in 2007.
Interpol investigating stolen passports on missing flight
Susan Sarandon 'very excited' about daughter's pregnancy