A US congresswoman shot in the head two weeks ago is moving to a Houston rehab centre today where her husband hopes she will continue on the path to a full recovery.

Democratic Rep Gabrielle Giffords has been making progress nearly every day in her recovery from a bullet wound to the brain.

Doctors ticked off markers of her continuing improvement: She scrolled through an iPad, picked out different coloured objects and moved her lips.

They are unsure whether she is mouthing words, nor do they know how much she is able to see.

Staff at University Medical Centre in Tucson took to Giffords a balcony at the hospital, where she breathed in the fresh air and felt the sun, trauma surgeon Peter Rhee said.

"I saw the biggest smile she could gather," Rhee said. "We are very happy to have her enjoying the sunshine of Arizona."

Her husband, Houston-based astronaut Mark Kelly, believes she has tried to speak and can recognise those around her.

"I can just look in her eyes and tell," Kelly said at a final briefing at the hospital. "She is very aware of the situation."

Today he tweeted: "GG going to next phase of her recover today. Very grateful to the docs and nurses at UMC, Tucson PD, Sheriffs Dept....Back in Tucson ASAP!"

Kelly said he hopes she'll make a full recovery.

"Congresswoman Giffords is a fighter," her aide C.J. Karamargin said on CBS television. "She's as tough as nails. She's communicated with her husband in positive ways," he added, calling it a sign that she'll be "back very soon. There's no question about it."

The doctors who will help her offered a more sober outlook.

"Not everyone always gets 100 % restoration, but we help them to get to a new normal," said Carl Josehart, chief executive of the rehab hospital that will be the Arizona congresswoman's home for the next month or two.

It's unclear if she is able to speak. And while she is moving both arms and legs, it's uncertain how much strength she has on her right side; the bullet passed through the left side of her brain, which controls the right side of the body.

A gunman shot Giffords and 18 other people on January 8 as she met with constituents outside a grocery store in Tucson. Six people died and the others wounded. All survivors, except Giffords, have been released from hospitals.

The suspect in the attack, Jared Loughner, 22, is being held in federal custody. His motives remain unknown.

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