TUCSON, Ariz. — The husband of Rep. Gabrielle Giffords said he would be willing to meet with the parents of the 22-year-old man accused in a massacre that critically injured the Arizona congresswoman, killed six people and wounded 12 others.

"I don't think it's their fault. It's not the parents' fault," Mark Kelly told ABC's Diane Sawyer in an interview to air Tuesday. "You know, I'd like to think I'm a person that's, you know, somewhat forgiving. And, I mean, they've got to be hurting in this situation as much as anybody."

The suspect, Jared Loughner, remained in federal custody in Phoenix. Investigators have described him as a mentally unstable man who was kicked out a community college last year and became increasingly erratic in recent months.

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He apparently became obsessed with inflicting violence on Giffords since attending one of her campaign events in 2007.

His parents, Randy and Amy, appeared in public together for the first time since the shooting Monday, having remained in seclusion since the shooting at a Safeway supermarket on Jan. 8, only releasing a statement that said they, too, were grieving for those dead and injured.

Kelly's comments were perhaps a sign of the nation's shock and outrage abating as the southern Arizona city buried the dead and Giffords made impressive strides toward recovery.

Giffords had given her husband, an astronaut who has kept a near-constant vigil by her bedside at a Tucson hospital, a neck rub and even smiled, he said.

Looking out for others
"She's in the ICU. You know, gone through this traumatic injury. And she spent 10 minutes giving me a neck massage," Kelly added. "It's so typical of her, that no matter how bad the situation might be for her, you know, she's looking out for other people."

The interactions with Kelly were the latest signs of Giffords' progress after being critically wounded in the attempted assassination 10 days ago. Giffords still cannot speak, because of a tube in her throat that is helping her breathe.

The movements indicate higher levels of functioning, implying that "she's recognizing him and interacting, perhaps in an old familiar way with him," said Dr. Michael Lemole.

Dr. Randall Friese said Kelly also told doctors Giffords had smiled. Friese said sometimes, people see what they want to see, but that "if he says she's smiling, I buy it."

Kelly's updates, along with his encouragement, have helped Giffords' staff through the tragedy, said Mark Kimble, a Tucson staff member who stood only a few feet from Giffords when she was shot.

"There is not a doubt in his mind, and not a doubt in any of our minds, that she's going to be back," Kimble said. "He's been cheering us up. He'll come over, and when we're down, he'll say, 'Gabby's going to make it, Gabby's a little better today.' That's a big help to all of us."

The New York Post published a photograph showing Loughner's parents leaving their house Monday, both wearing dark sunglasses.

They visited a building that houses the offices of the federal defender, the Post said, adding that they refused to talk to reporters when leaving the building and returned home following a stop to get a pizza.

"You don't know what they're going through, but you can guess," George Gayan, 82, a neighbor, told the newspaper.

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Doctors upgraded Giffords' condition from critical to serious over the weekend and say they carried out three successful procedures that demonstrate she was recovering well.

A breathing tube was moved from her mouth to her throat along with a separate feeding tube that was shifted from her nose to her stomach. Friese said removing the tubes in her nose and mouth reduces the risks of infections.

Doctors also said they performed a surgery on Giffords' eye socket to remove bone fragments to relieve pressure on her eye.

No complications arose from the surgery; doctors needed to perform the eye procedure all along but waited until her condition improved to do it.