Capitol Police have reached out to members of Congress to ensure they were taking "reasonable and prudent precautions," according to a spokesperson.
Giffords was shot in the head on Saturday morning in Tucson while meeting with constituents in front of a grocery. Six people were killed -- including a 9-year-old girl, a Giffords aide and a federal judge -- and 19 were injured.
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Giffords spokesman C.J. Karamargin said three Giffords staffers were shot, the Associated Press reported. Gabe Zimmerman, a former social worker who served as Giffords' director of community outreach, died. The other two are expected to survive.
While Capitol Police did not name specific security measures, the force said they had contacted members of Congress to tell them to raise their vigilance.
"The United States Capitol Police remains at a high level of readiness," Sgt. Kimberly Schneider said in a press release, "consistent with our operating conditions on U.S. Capitol Grounds, and we maintain a robust presence."
Capitol Police said the shooter had been arrested. The suspect is 22-years-old and used a pistol to carry out the attack. MSNBC reported the name of the suspect is Jared Laughner.
Authorities said they believe that Giffords was the target and that the gunman arrived at the scene with another person. They are looking for that person.
Legislators from around the region have expressed disgust for the violent assault. "I was deeply horrified to learn today of the shooting of Representative Gabrielle Gifford," said House Majority Leader Eric Cantor, (R-VA). "Our thoughts and prayers are with Congresswoman Giffords and her family, her staff, and the residents of Tucson on this sad day."
Congresswoman Donna F. Edwards (D-MD) also offered words of support for Giffords. "I am shocked and saddened to learn of the horrible act of violence committed against Congresswoman Giffords, members of her staff, and her constituents," she said. "She is a beloved Member of Congress, a dedicated public servant, and a true friend."
In a press conference, Dr. Peter Rhee of University Medical Center in Tucson updated Giffords' condition. Rhee said that Giffords had sustained a bullet wound "through and through" the head. Despite the severity of her injury, Rhee said that she was responsive to commands and he was "very optimistic" about her chances for recovery.
Capitol Police are working together with other federal and local authorities in the ongoing investigation.