Her family and doctors report she can understand and respond to questions, and she can mouth the lyrics to easy songs.
"The communication is coming back very quickly," Mark Kelly said.
Kelly said she is trying so hard that her speech therapist, who only a few days ago was trying to get her to talk more, is now asking Giffords to slow down and make sure she hears the question before giving an answer.
The congresswoman even spoke briefly on the phone with her brother-in-law aboard the International Space Station, according to the New York Times.
Giffords was shot in the head on January 8 while meeting with constituents in Tucson. Six people were killed in the attack, including a 9-year-old girl and a federal judge.
The Associated Press contributed to this story.