Doctors say Arizona congresswoman Gabrielle Giffords is making gradual progress as she recovers from being shot in the head last weekend.

Dr. Michael Lemole, the neurosurgeon involved in the congresswoman's case, told reporters Friday that Giffords is able to respond to more and more "complex sequences" that she is presented with.

"We're very encouraged that she is continuing to make all the right moves in the right direction," Lemole said.

"Obviously, we're very cautious that she makes them at her own pace. But again, we couldn't have hoped for any better improvement than we're seeing now given the severity of her injury initially.

Giffords was one of 14 wounded in a mass shooting outside an Arizona shopping centre last weekend. Six people died in the violence.

Since landing in hospital, Giffords has managed to open her eyes, move her limbs and give her physicians and family hope that she is going to continue to make progress.

By Wednesday, only four days after the attack, Giffords opened her left eye and tried to focus on the people around her.

Lemole previously said that moment was "a major milestone" that indicated she was responding to the friends and family that had gathered around her.

Her husband, NASA astronaut Mark Kelly, reported on his Twitter feed Friday that his wife "has been improving each day," and he thanked the public for their messages of support.

Kelly is supposed to lead the space shuttle Endeavour on its final trip into space later this year.

But because of the trauma that his wife has gone through, NASA has named a stand-in for Kelly in the event he is not able perform his duties.

NASA's chief astronaut Peggy Whitson said Kelly "is facing many uncertainties now as he supports Gabrielle, and our goal is to allow him to keep his undistracted attention on his family while allowing preparations for the mission to progress."

At the same time that Giffords is recovering in hospital, other families are burying their dead in the wake of the deadly attack in Arizona.

A funeral for U.S. District Judge John Roll was held in Tucson on Friday. Security was tight at his memorial, with U.S. marshals checking the identification of each person entering the parking lot of the church where the service was held.

Roll was 63 years old when he was gunned down last weekend.

A nine-year-old girl was laid to rest in Arizona on Thursday. Christina Green was born on the day that the World Trade Center towers were attacked and she was gunned down during the mass shooting.

Green was one of the members of the public who had attended a "Congress on Your Corner" event Giffords was holding at an Arizona shopping centre last Saturday. The event was being held to allow constituents to meet Giffords and ask her about issues concerning the government.

The man accused of the shooting is currently being held at a prison in Phoenix, according to information listed on the U.S. Bureau of Prisons website.

Jared Lee Loughner currently faces five federal charges: the attempted assassination of a member of Congress, two counts of killing an employee of the federal government and two counts of attempting to kill a federal employee. The 22-year-old suspect is expected to face further charges from the state of Arizona.

With files from The Associated Press