Six people died in the shooting rampage and wounded 14.
Up until Saturday's tragic shooting, Kelly had been training to command NASA's last space shuttle flight, scheduled for April.
Kelly was in Texas when the shooting occurred and he rushed to be with his wife.
On Sunday, Kelly released the following statement: "On behalf of Gabby and our entire family, I want to extend our heartfelt gratitude to the people of Arizona and this great nation for their unbelievable outpouring of support. Gabby was doing what she loved most - hearing from her constituents - when this tragedy occurred. Serving Southern Arizonans is her passion, and nothing makes her more proud than representing them in Congress."
Doctors on Monday said they have "a lot of hope" for Giffords' recovery as she is following and communicating through commands.
ABC News' Cameron Brock and Leezel Tanglao contributed to this report.