Six people, including a 9-year-old, were killed, and 13 others, including Gifford, survived after a gunman opened fire on a public-meet-and-greet organized by the representative. One of those killed was U.S. District Court Judge John M. Roll, a friend of Giffords' who had come to visit her at the event.
The Democrat, who had been critical of Arizona's controversial immigration law and a proponent of health-care reform, was said to have received a through-and-through gunshot wound to her head but was expected to recover.
"Today is a very sad day for all those who have devoted their lives to public service, regardless of affiliation or ideology. Congresswoman Gabrielle Giffords is a tenacious fighter who has served the 8th District of Arizona with the same courage and strength she is demonstrating today.
"My thoughts and prayers are with Congresswoman Giffords' family and staff members and I wish her a speedy and full recovery. My heart goes out to the families of all the victims of this senseless act of violence."
Some speculation about the attack pointed to Sarah Palin's listing of Giffords as someone she would like to have unseated. Palin's people used a graphic target to denote Giffords' district in literature.
Pima County Sheriff Clarence Dupnik criticized what he said was the nation's increasing vitriol when it comes to political discourse and that this kind of hatred contributed to an "unstable" suspect's actions.
"The hatred and bigotry in this country have gotten out of control," he told reporters.
He said Arizona has "become the mecca for prejudice and bigotry."
The suspect was identified as 22-year-old Jared Lee Loughner. Dupnik also said an older man connected somehow to Loughner was being sought.
Dupnik said they had a photo of that man but that they could not yet release it.
Witnesses said the suspect walked up to a crowd outside a Safeway that had gathered to see Giffords and opened fire, apparently targeting Giffords first. Dupnik said two bystanders tackled and held the suspect before authorities arrived.
The man was being held and had invoked his right to remain silent.
A self-described classmate of Loughner described him as a "left wing ... pot head."
"He has kind of a troubled past, I can tell you that," the sheriff said, adding that authorities don't believe he acted alone.
Dupnik said Giffords had received death threats, but it wasn't clear if there was any link to the suspect.
In June Giffords sent a letter to L.A. city officials asking them to back off of its economic boycott of Arizona over the immigration law, saying such a move would actually hurt immigrant workers.
While Giffords critical of the state's law, which would have police ask suspects who might appear to be illegal immigrants for their papers, she also persuaded the Obama administration to order 1,200 National Guard troops to head to the border to help border patrol agency stem the tide of illegal immigration.
More from our sister publication the Phoenix New Times.