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Democratic Representative Gabrielle Giffords, 40, was shot in the head at close range in front of hundreds of people in Tucson.
She and four other people are in a critical condition, a hospital doctor told reporters. He said he was "very optimistic about her recovery".
A man was arrested by police after the shooting. The motive remains unclear.
The Associated Press news agency reports that a federal judge and one of Ms Giffords' political aides were killed in the shooting.
Several other people received "non-life-threatening" injuries in the shooting.
President Barack Obama has described the events in Tucson as "an unspeakable tragedy".
'Senseless'
Ms Giffords, 40, who represents the eighth district of Arizona in the US House of Representatives, is married to space shuttle astronaut Mark Kelly.
She has served on several congressional committees, including those covering the armed services and foreign affairs.
Jeff Rogers, chairman of the local Democrats, told BBC News that Ms Giffords was "a rising star" in the party with hopes of eventually winning the Arizona Senate seat.
He described her as "a wonderful congresswoman and a wonderful person", adding: "We just can't continue to have this kind of carnage on school campuses and against public officials."
In a statement issued by the White House, President Obama said: "This morning, in an unspeakable tragedy, a number of Americans were shot in Tucson, Arizona, at a constituent meeting with Congresswoman Gabrielle Giffords.
"And while we are continuing to receive information, we know that some have passed away, and that Representative Giffords is gravely wounded.
"We do not yet have all the answers. What we do know is that such a senseless and terrible act of violence has no place in a free society.
"I ask all Americans to join me and Michelle in keeping Representative Giffords, the victims of this tragedy, and their families in our prayers."
The Speaker of the House or Representatives, John Boehner, said: "I am horrified by the senseless attack on Congresswoman Gabrielle Giffords and members of her staff.
"An attack on one who serves is an attack on all who serve. Acts and threats of violence against public officials have no place in our society. Our prayers are with Congresswoman Giffords, her staff, all who were injured, and their families. This is a sad day for our country."
Holy shit. I knew some of the right-wingers were were nuts, but damn.