Gabrielle Giffords, shot in the head as she addressed her supporters in Tucson, Arizona, was briefly revived from anesthesia, a source close to the family told the Politico newspaper Saturday night.
The congresswoman recognized her husband, astronaut Mark Kelly, before slipping back into unconsciousness, the source said, RIA Novosti reported.
Giffords, 40, was shot point-blank and hospitalized in a critical condition. She underwent brain surgery, and doctors said they were "cautiously optimistic" about her recovery.
Arizona police said six people were killed and 13 others were wounded in the shooting spree. U.S. District Judge
John Roll, Giffords' aide and a 9-year-old girl were among those killed.
Giffords is known as a moderate centrist politician and a rising star among American lawmakers. A third-term Democrat in the U.S. House of Representatives, she supported the right of Americans to bear arms and criticized existing immigration laws.
The suspect, who was apprehended at the scene, has been identified as a 22-year-old Jared Lee Loughner of Arizona. He used a 9-mm semi-automatic handgun in the attack.
Police said the suspect might have had an accomplice who fled the scene after the shooting started.
Barack Obama called the shooting a "senseless and terrible act of violence" and an "unspeakable tragedy."