Shot US congresswoman in critical condition
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A nine-year-old girl and a federal judge were among those killed, and 12 others were wounded.
Obama called the attack a "tragedy for our entire country." The House of Representatives, which opened under new Republican leadership just three days earlier, called off proceedings for the upcoming week.
Bystanders tackled down the gunman, identified as 22-year-old local resident Jared Lee Loughner. News reports said he had filled the Internet with angry and largely incoherent condemnations of the government, while the army said he had tried to enlist but was rejected.
A Loughner profile posted on YouTube listed Karl Marx and Friedrich Engels's "The Communist Manifesto" and Adolf Hitler's "Mein Kampf" among his favourite books.
"There's some reason to believe that he came to this location with another individual," Sheriff Clarence Dupnik told reporters, saying the gunman "has kind of a troubled past, and we're not convinced that he acted alone."
Doctors said a bullet passed through Giffords' brain. Despite initial media reports she had died, local television networks said late Saturday she was awake in her hospital bed and recognized her husband, NASA astronaut Mark Kelly.
"She is in critical condition (but) I'm optimistic about recovery," said University Medical Center trauma chief Peter Rhee. "We cannot tell what kind of recovery, but I'm about as optimistic as you can get."
At a later briefing however, Giffords family friend and former US surgeon general Richard Carmona was more cautious, saying: "With guarded optimism I hope that she will survive, but this is a very devastating wound."
Giffords was hosting an event dubbed "Congress on Your Corner" at a Safeway supermarket in a strip mall off a major intersection in Tucson.
Giffords, like most rank-and-file US legislators, traveled without any security detail, according to witnesses.
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