Loughner reportedly was wrestled down after at least 18 people were shot by a gunman outside an event at a Safeway. At least six have died.
Pima County Sheriff Clarence Dupnik confirmed Saturday that Giffords was the shooter's target, and said he is not ruling out a conspiracy. "We're not convinced he acted alone," Dupnik said, adding: "He came to this location with another individual."
The FBI is heading the investigation of the shootings; on Saturday evening, the agency's director, Robert Mueller, headed to Arizona to oversee the work personally.
"We still don't know what provoked this attack," said President Obama, at a news conference Saturday afternoon, describing Giffords a friend of his.
"This is a tragedy for Arizona, and a tragedy for our entire country," he said.
U.S. Capitol Police, meanwhile, urged other members of Congress to "take reasonable and prudent precautions regarding their personal safety and security." Arizona Gov. Jan Brewer acknowledged that politicians appear to be endangered. There are "disturbed people in society,' and "sometimes those of us in elected positions are the target," said Brewer, a Republican.
Police said at a news conference that the gunman came up to Gifford from behind and shot her in the head.
Investigators have recovered a pistol with an extended magazine, according to Pima County Sheriff's Deputy Rich Kastigar. They do not know how the shooter got to the scene, and were seeking videos from nearby stores and shops. Kastigar also said police had not had previous contact with Loughner, at least as an adult, but suggested there might have been previous contact of some sort.
There was no phone number listed under his name in the Tucson area.
But a Jared Loughner - it cannot yet be confirmed he is the same man - has left a troubling Internet trail of anti-government comments and tirades.
Samples of videos on what may be his YouTube sites include comments that he "can't trust the current government because of the ratifications: the government is implying mind control and brainwash on the people by controlling grammar."
He also rants against currency not backed by gold and silver, saying, "No! I won't pay debt with a currency that's not backed by gold and silver!" and adding: "No! I won't trust in God!"
A MySpace page that may also belong to Loughner but that became inaccessible in the hours after his arrest, lists lists Nazi leader Adolph Hitler's biography, Mein Kampf, and The Communist Manifesto by Karl Marx, as well as books dealing with totalitarianism and mind control: Brave New World, Animal Farm, and Farenheit 451.
Cameron Joseph and Lindsey Boerma contributed to this report.