The husband of shot US congresswoman Gabrielle Giffords says his wife's condition has improved so much that she has been able to smile and give him a neck rub at her hospital bedside.

The interactions with astronaut Mark Kelly are new signs of the Arizona Democrat's impressive progress in recovering from the assassination attempt which happened as she held an open-air surgery on January 8.

The mass shooting outside a Tucson supermarket left six dead and 13 others wounded, including Ms Giffords, who was shot in the head.

But Ms Giffords, 40, still cannot speak because of a tube in her throat that is helping her breathe.

"She's in the (intensive care unit). You know, gone through this traumatic injury. And she spent 10 minutes giving me a neck massage," Mr Kelly says in an interview to be shown on ABC today.

"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."

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

Dr Randall Friese said Mr Kelly also told doctors he saw Ms Giffords smile. He said sometimes people saw what they wanted to see, but that "if he says she's smiling, I buy it".

Mr Kelly has also been essential in helping Ms Giffords' staff through the tragedy, said Mark Kimble, a Tucson staff member who stood only a few feet from the politician 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.

"He's (Mr Kelly) 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."

News of Ms Giffords' steady progress came poignantly on the Martin Luther King national holiday to remember the legacy of the civil rights leader who was killed by an assassin's bullet 42 years ago.

Political leaders invoked the assassination attempt against Ms Giffords as they asked Americans to recommit to the King values of non-violence, tolerance, compassion and justice.

"Last week a senseless rampage in Tucson reminded us that more than 40 years after Dr King's own tragic death, our struggle to eradicate violence and to promote peace goes on," US attorney general Eric Holder, who is black, said at Dr King's former church in Atlanta, Georgia.

Doctors upgraded Ms 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. Dr Friese said removing the tubes in her nose and mouth reduces the risks of infections.

Doctors also said they performed a surgery on an eye socket to remove bone fragments to relieve pressure on the eye.

The shooting suspect, 22-year-old Jared Loughner, remained behind bars in Phoenix. Investigators have described him as a mentally unstable man who was kicked out of a community college last year and became increasingly erratic in recent months.

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

Mr Kelly said he would be willing to meet Loughner's parents, who have remained in seclusion since the shooting. Mr Kelly, who has two teenage daughters from a previous marriage, said they had to be in a tremendous amount of pain.

"I don't think it's their fault. It's not the parents fault," he told ABC. "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 much as anybody."

Meanwhile more details emerged about one of the shooting victims who became distraught and was arrested after an outburst at a televised town hall meeting.

James Fuller, a military veteran and self-described liberal, started ranting at the end of the programme on Saturday. He took a picture of the Tucson leader of the conservative tea party movement, Trent Humphries, and yelled: "You're dead."

Mr Fuller, who has been in a hospital since being involuntarily committed on Saturday for a mental health evaluation, apologised to Mr Humphries yesterday for his "misplaced outrage".

It also emerged that the corneas donated from the nine-year-old girl killed in the mass shooting have saved the eyesight of two children.

Christina Taylor Green's father John said the Donor Network of Arizona told him and his wife about the successful transplants.