The medical team at University Medical Center in Tucson said they were "cautiously optimistic," CNN reported.
At a news conference, Dr. G. Michael Lemole Jr., chief of neurosurgery, said Giffords has responded to simple commands. He told CNN Giffords' responses suggest she has retained the ability for higher levels of reasoning.
Lemole, who operated on Giffords, said the bullet passed through the left side of her brain "back to front," causing less damage than it would have going through both hemispheres.
Giffords was in a medically induced coma.
"When you get shot in the head and a bullet goes through your brain, your chances of living are very small," said Dr. Peter Rhee, chief of trauma surgery.
Giffords, believed to be the shooter's target, was the only one of the wounded to remain in critical condition. Six people were killed.
Jared Lee Loughner, a 22-year-old Tucson man, has been charged with the mass shooting.
Notable deaths of 2014 [PHOTOS]