Space shuttle commander Mark Kelly wouldn't go into details about her condition during a news conference Friday, and deflected questions about how he knows she supports his choice to fly.
"I know her very well and she would be very comfortable with the decision that I made," he said.
Kelly took a leave from training after Giffords was gunned down in Tucson, Ariz., on Jan. 8. NASA announced earlier Friday he would resume training for space shuttle Endeavour's two-week mission, which is targeted for liftoff from Cape Canaveral, Fla., on April 19.
When asked if Giffords might be well enough to attend his launch, Kelly said: "Absolutely. I have every intention that she'll be there for the launch. I've already talked to her doctors about it."
It will be Endeavour's final flight and the fourth spaceflight for Kelly.
Kelly said the congresswoman continues to improve in rehab in Houston. One doctor has described her recovery as "lightning speed." She's kept very busy with therapy, a key to his decision, he said.
The 40-year-old Giffords was in intensive care for two weeks in Arizona, with Kelly at her bedside, before she was transferred to Houston for what is expected to be a lengthy rehabilitation. Kelly wanted her as close to him as possible, if he returned to work at Johnson Space Center. He lives in the Houston area with his two teenage daughters from a previous marriage, Claudia and Claire.
Giffords was meeting with constituents outside a Tucson supermarket when she was shot in the head. Six people were killed and 13 were injured in the rampage; a 22-year-old suspect is in custody.
Giffords' wound was devastating, and Kelly, 46, said he initially expected to step down as commander of Endeavour. In the meantime, NASA named a backup commander, Rick Sturckow, who joined the crew for training. Kelly said all along that he wanted his wife's input in the matter, if at all possible.
Though doctors described her early progress as remarkable, they have said very little about her condition, including whether she's able to speak. She was shot in the left side of her brain and doctors have said she had weakness on her right side.
In the first several days after the shooting, she gave a thumbs up and was able to stand with help. She massaged her husband's neck, picked out colors on an iPad and playfully took the ring off a nurse's finger. Friends and Kelly described her as able to understand them.
Her hospital, TIRR Memorial Hermann, last week said it would not provide any more information on her condition. In a Twitter update Wednesday, her husband said Giffords is making "Lots of progress!"
"I'm not going to second guess his decision for anything. I respect his decision, I'm sure it's the decision that Gabby would have wanted him to make and I'm sure he has the support of his family and friends there," said former astronaut Susan Still Kilrain, who gave up her astronaut career when she had the first of her four children.
Kelly - whose identical twin Scott currently is commander of the International Space Station - will lead a veteran, all-male, American-Italian crew to the space station. Scott Kelly will be back on Earth by then.
There's considerable training between now and liftoff, almost certainly with long hours and few days off for the crew. The six astronauts will go into quarantine a week before the launch, with limited access to family members.
"I obviously weigh time that I can spend with her, with what I think is in the best interest of NASA and my crew. So that's a debate I had with myself," Kelly said.
Kelly's mission already was set to be one of the highest profile shuttle flights ever. It will be Endeavour's last voyage and the next-to-last for the entire 30-year shuttle program, and will feature the delivery of an elaborate physics experiment by a Nobel prize winner.
Endeavour was originally scheduled to launch last July, but was bumped into 2011 because the experiment wasn't ready.
Susan Hileman, who was wounded in Tucson, trusts Kelly's decision. She was holding 9-year-old Christina Green's hand when the shooting erupted. The girl was killed.
"I'm sure this decision was carefully made and thoughtfully made, and right for him and for them," said Hileman, who was shot three times. "He's kind and thoughtful and he loves his wife as much as my husband loves me, which is a lot, and we're both lucky women to have such strong men in our lives."
Rabbi Stephanie Aaron, who married Giffords and Kelly in 2007, said the couple has been communicating but she didn't elaborate.
"I think that once he saw that Gabby was so strong and on the mend .... that he made the decision based on, I'm sure, what her wishes would be," Aaron said.
AP writers Seth Borenstein in Washington and Amanda Lee Myers in Phoenix and video producer Tom Ritchie in Washington contributed to this report. Dunn reported from Cape Canaveral, Fla.