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," Kelly said.
Kelly stepped down from training after Giffords was gunned down in Tucson, Ariz., on Jan. 8. His decision to resume training for space shuttle Endeavour's mission was announced earlier Friday.
He said he plans for his wife to be at Cape Canaveral, Fla., for liftoff, targeted for April 19.
"I have every intention that she'll be there for launch. I've talked to her doctors about that," he said.
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.
Kelly, 46, said he initially expected to step down as commander of Endeavour. As he agonized over the decision, 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.
Specific details of Giffords' recovery have not been released, including whether she's able to speak. Last week, doctors said she would have a valve inserted into her breathing tube to help her talk. They said she could breathe on her own but they weren't going to remove the tube immediately. She was shot in the left side of her brain and doctors have said she had weakness on her right side.
Her hospital, TIRR Memorial Hermann, last week said it would not provide any more information on her condition. In a Twitter update Wednesday, Mark Kelly said Giffords is making "Lots of progress!"
Kelly - whose identical twin Scott currently is commander of the International Space Station - has flown three times aboard space shuttles. He will lead a veteran, all-male, American-Italian crew to the International Space Station.
There's considerable training between now and the April 19 launch target date, 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 weighed time I could spend with her over time I could spend with NASA and my crew," he said on Friday.
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.
"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.
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.