The 22-year-old is charged with the attempted assassination of U.S. Rep. Gabrielle Giffords and the attempted murder of two of her aides. He is accused of opening fire on a Giffords political event at a Safeway grocery store in Tucson. A federal judge and a 9-year-old girl who was born on Sept. 11, 2001 were among those who lost their lives.
Loughner will later face state charges dealing with the other victims.
Meanwhile, the Houston hospital treating Giffords said Sunday that her condition is improving daily, but gave no update on the buildup of brain fluid that has kept the Arizona congresswoman in intensive care.
Federal agents building a case against Loughner have searched his home and questioned people who knew him, including employees at a tattoo shop, where Loughner inquired about a tattoo of a bullet.
"I told the FBI that all he was talking about was his crazy dreams and how he knew how to control them," said tattoo artist Brittany Ramirez.
Experts said Loughner's lawyers will likely mount an insanity defense.
Prosecutors haven't signaled if they would pursue the death penalty.
Also, papers were filed Sunday night requesting the case to be transferred back to Tucson where all the victims and witnesses live.
The case was moved to Phoenix because one of the six dead, U.S. District Judge John Roll, was based in Tucson and federal judges there recused themselves. All the federal judges in the rest of the state soon joined them, and a San Diego-based judge is now assigned to the case.
The Associated Press contributed to this report.