Loughner, right, has been charged with murder and anttempted murder over the shooting [EPA]

The family of the man charged with a shooting spree that left six people dead and 14 others injured in the US state of Arizona has expressed sorrow and shock at the rampage.

"There are no words that can possibly express how we feel. We wish there were, so we could make you feel better," read a statement released by the family of Jared Lee Loughner on Tuesday.

Loughner has been charged with murder and attempted murder over the attack with a semi-automatic pistol on a political event being held by Gabrielle Giffords, a US congresswoman, outside a supermarket in the city of Tucson.

"We don't understand why this happened. It may not make any difference, but we wish that we could change the heinous events of Saturday," the eight-sentence statement from the Loughners handed to journalists said.

"We care very deeply about the victims and their families. We are so very sorry for their loss."

Giffords remained in a critical condition in hospital on Tuesday after being shot in the head in the attack but was "holding her own," responding to simple commands and breathing without the aid of her ventilation tube.

"She has no right to look this good. We're hopeful," Dr Michael Lemole, the head of neurosurgery at the University Medical Center, said.

"It's week to week, month to month," he said. "She's going to take her recovery at her own pace."

Barack Obama, the US president, will travel to Arizona on Wednesday to attend a memorial service for the dead, who included a federal judge, a nine-year-old girl and one of Giffords' aides.

Al Jazeera's Franc Contreras, reporting from Tucson, said Obama would deliver a message of reconciliation and hope.

"He is going to have to walk a very thin political line because previous presidents have had to confront such disasters, such national tragedies, and every time they do ... it can be perceived as politicians trying to make benefit from it," he said.

Source: Al Jazeera and agencies