Mark Kelly said in an interview broadcast Monday on NBC that he can ask his wife questions and she can respond.
"The communication is coming back very quickly," he 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.
As an example, Kelly spoke of a time when the therapist had three cards on a table, one with a picture of George W. Bush, one with a picture of President Barack Obama and another with an image of George Washington.
"Before she was asked a question, she'd picked up the card and held it up and said 'George Bush,'" Kelly told NBC's Brian Williams. "She's a hard worker and she's trying. She's speaking a lot and at some level they are asking her to slow down a little bit."
The New York Times, citing doctors and her staff, reported on its website late Sunday that Giffords' efforts to relearn how to speak have included mouthing song lyrics, such as "Twinkle, Twinkle, Little Star" and "Happy Birthday to You," as friends and family sang along.
Giffords also briefly spoke with her brother-in-law Scott Kelly by telephone Sunday afternoon as he orbited aboard the International Space Station.
"She said, hi, I'm good," her chief of staff, Pia Carusone, told the paper. He is the brother of Giffords' husband, who is also an astronaut.
She has also been receiving bedside briefings from aides on the recent uprising in Egypt and on last week's decision by Republican Sen. Jon Kyl of Arizona not to seek re-election,
"We tell her everything that's going on," Carusone said. "Don't get the idea she's speaking in paragraphs, but she definitely understands what we're saying and she's verbalizing."
Giffords was shot in the head Jan. 8 while meeting with constituents outside a Tucson grocery store. Six people, including a 9-year-old girl and a federal judge, were killed in the attack, and 13 others, including Giffords, were wounded.
The congresswoman began intensive rehabilitation at TIRR Memorial Hermann in Houston late last month. The Times reported that an e-mail sent to friends about a week ago by Giffords' mother said that Giffords has been doing squats and repetitive motions to build her muscles and walking through the hospital's halls while holding onto a cart.
The 40-year-old Giffords has beaten one of her nurses at tic-tac-toe and has changed from "kind of a limp noodle" to someone who is "alert, sits up straight with good posture," the e-mail from Gloria Giffords said.
Doctors said in late January that they planned to insert a speaking valve into her tracheostomy - a tube inserted into Giffords' throat to assist her breathing immediately after the shooting. Her doctors have not said whether that procedure took place or whether the tube was removed since she no longer needs it.
Rehabilitation specialists say brain injury patients who regain speech typically begin to do so about four to six weeks after the incident. Several news organizations reported last week that Giffords asked for toast with her breakfast one recent morning.