U.S. District Judge Nicholas Burns ruled Monday Loughner should continue treatment at the federal medical facility in Springfield, Mo., The Arizona Republic reported. Burns said the psychologist responsible for Loughner's treatment has reported progress but says he is "not there yet."
Burns extended Loughner's stay in Springfield through June 7 unless the psychologist decides earlier he can assist in his own defense.
Loughner did not attend the hearing in San Diego. Federal prosecutors in Tucson participated through a video link.
Giffords, D-Ariz., recently said she would not run for another term. She suffered a severe head injury in the January 2011 shooting.
Twelve other people suffered less serious injuries. Those killed included a federal judge, a 9-year-old girl and a member of Giffords' staff.