Doctors said Giffords, D-Ariz., is blinking, focusing her eyes on her husband, and has smiled at him, the Arizona Daily Star in Tucson reported Tuesday.
While her prognosis is unknown, doctors at University Medical Center in Tucson said Giffords' is making a "miraculous" recovery from her head injury sustained Jan. 8 during her "Congress on the Corner" meet-and-greet with constituents at a Tucson grocery store. Six people died and 13 people, including Giffords, were injured.
She is one of three patients still hospitalized. On Sunday, the hospital upgraded Giffords' condition from critical to serious. Two patients are in good condition.
Giffords successfully underwent an operation during the weekend to repair a fracture in the roof of her right eye socket and is "back at that same baseline where she was before surgery," said Dr. Michael Lemole, chief of neurosurgery at University Medical Center.
Asked about when Giffords could be released from the hospital and admitted into a rehabilitation center, Lemole said it could be as soon as "days to weeks," CNN reported.
"At this time, we're hoping to continue tying up those loose ends and get her ready for that third phase of her care -- the rehabilitation," Lemole said. "The family is looking at all their resources. They have the entire country available. It has to be in a place that is not only top-notch in terms of the ability to render care and rehabilitation, but also proximity to family is very important."
Doctors removed a breathing tube from Giffords' nose, inserting a second one into her neck, trauma surgeon Dr. Randall Friese said.
A feeding tube also was inserted, doctors said.
Asked about reports that Giffords gave her husband, NASA astronaut Mark Kelly, a neck rub, Lemole said, "there's a lot of inference there," adding, "it does imply that she's recognizing him," CNN said.
Doctors do not know whether she can see out of both eyes, he said, pending a thorough examination.
The other two patients still hospitalized are close to being discharged, he said.