Pima County Sheriff Clarence Dupnik said a 22-year-old was in custody after the shooting rampage. He would not identify the suspect, but people familiar with the investigation said.
Officials say he has claimed sole responsibility for the attack, but said authorities were "not convinced he acted alone," Dupnik said.
Dupnik said authorities had "some reason to believe he came to the event with another individual," and said investigators had pictures of the other "person of interest." Dupnik would say the person appeared to be around 50 years old.
Giffords, D-Ariz., was shot in the head in an area where the lawmaker was meeting with constituents. Pima County Sheriff Clarence Dupnik said authorities believe she was the target and that there was no security at the event.
The shooting rampage claimed six lives, including a 9-year-old child and U.S. District Judge John Roll, officials said. Thirteen more were wounded at the scene, including Giffords. Five were listed in critical condition and five were in serious condition. All had come out of surgery by Saturday evening.
Giffords was one of those in critical condition, but hospital officialsshe would survive the wound.
The assailant fired into an area where the Democratic lawmaker was hosting a "Congress on Your Corner" event at a Safeway supermarket.
"The gunman began just spraying everybody at point blank range. It wasn't like he was picking people out, he just began shooting at everybody who was close to him and kind of a constricted area," Dr. Steven Rayle, who witnessed the shooting and offered medical attention to the victims, told CBS News.
Rayle said the suspect "had a determined look on his face. And he just began shooting, wearing dark clothes, a little bit ... shabbily dressed, and he really, I think ... thought he would be getting away."
Two people at the scene tackled the suspect, officials said. Dupnik said "he probably would have shot other people had he not been tackled."
CBS News correspondent Bob Orr reports that the gun recovered at the scene is a 9mm Glock pistol. Sources earlier said it was equipped with an extended magazine. There is no word on the number of rounds fired.
The suspect's exact motivation was not immediately clear. Federal law enforcement officials were poring over captured versions of a MySpace page that belonged to Jared Loughner and over Youtube video published to the Internet weeks ago under an account "Classitup10" and linked to him. The MySpace page, which was removed within minutes of the gunman being identified by U.S. officials, included a mysterious "Goodbye friends" message published hours before the shooting and exhorted his friends to "Please don't be mad at me."
In one of several Youtube videos, which featured text against a dark background, Loughner described inventing a new U.S. currency and complained about the illiteracy rate among people living in Giffords' congressional district in Arizona. Two spellings of his last name were given in the aftermath of the shooting -- Loughner and Laughner.
"I know who's listening: Government Officials, and the People," Loughner wrote. "Nearly all the people, who don't know this accurate information of a new currency, aren't aware of mind control and brainwash methods. If I have my civil rights, then this message wouldn't have happen (sic)."
Without identifying the suspect, Dupnik said he "has kind of a troubled past, I can tell you that."
The FBI has joined the investigation of the attack.
Members of Congress do not have Secret Service protection. They are protected by U.S. Capitol Police on the Hill, but they have to provide their own security - if any - in their home districts.