The space agency emphasized that Capt. Mark Kelly, Giffords' husband of more than three years, remains the commander for the final scheduled flight of the space shuttle program. The shuttle Endeavour is scheduled to launch April 19 on a trip to the International Space Station.
Kelly said in a written statement released by NASA that he recommended to the space agency that it should "take steps now to prepare to complete the mission in my absence if necessary." Giffords, Kelly's wife, was gravely wounded by a gunman last Saturday.
Chief astronaut Peggy Whitson said the move allows Kelly to keep his attention on his family.
Special Section: Tragedy in Tucson
Meanwhile, doctors said Giffords continued making strong progress toward recovery.
Giffords, 40, is , has and is responding to friends and family, doctors said Thursday. They've helped her sit up and dangle her legs from the bed, and she is able to lift her legs on command.
"Gabby, Open Your Eyes"; Friends Recount Scene
With her closest friends from Congress holding her hand Wednesday evening, Giffords opened her left eye and tried to focus on loved ones for the first time.
"It was raw courage. It was raw strength. It was so beautiful and so moving," Sen. Kirsten Gillibrand of New York said of the Arizona legislator. "She wanted us to know that she was with us a hundred percent and understood everything we were saying."
Rep. Giffords Recovery: Moving Legs and Arms
Giffords' neurosurgeon, Dr. Michael Lemole, called it "a major milestone," and said the congresswoman was clearly responding to the gathering of friends and family.
After five days of pushing for caution, Lemole acknowledged: "We're wise to acknowledge miracles."