Spokesman C.J. Karamargin said Giffords is speaking "more and more" as she continues rehab at a Houston hospital. Giffords spoke for the first time a few days ago.
It's unknown what her very first words were, but she reportedly asked for toast for breakfast one morning.
The news is the first confirmation that Giffords is able to talk after being shot last month during an attack outside a grocery store where Giffords was meeting with constituents. Six people were killed in the attack, including a 9-year-old girl and a federal judge.
In a Facebook post on Tuesday, Giffords' husband Mark Kelly said his wife had her appetite back and was eating three times a day, "even though it's hospital food."
"It is hard to believe that only one month has passed since Gabrielle was shot," he wrote. "The doctors say she is recovering at lightning speed considering her injury but they aren't kidding when they say this is a marathon process."
The Associated Press contributed to this story.