The 22-year-old man accused of attempting to assassinate a Jewish US congresswoman from Arizona and of killing six others has appeared in court.

Jared Loughner was in a Phoenix court yesterday, two days after he allegedly rampaged through a supermarket as Congresswoman Gabrielle Giffords met constituents at a routine political event.

He was told by the judge that he could face either life behind bars, or the death penalty, for the shooting spree, which also left 14 people injured.

Among the dead were a federal judge, Ms Gifford’s congressional aide and a nine-year-old girl, born on the day of the September 11 attacks.

Ms Giffords, who was shot directly in the head at close range, remains in intensive care and on a ventilator, but her doctors said she was responding to verbal commands and showing movement in her fingers and toes.

Neurosurgeon Dr Michael Lemole said: "We're not out of the woods yet.

“Every day that goes by and we don't see an increase [in swelling on her brain], we're slightly more optimistic."

But he added: “It could go either way."

Mr Loughner is also facing two charges for killing a federal government employee and another for attempting to kill a federal employee. Described by those who know him as a loner, he is being defended by Judy Clarke, formerly the lawyer for the "Unabomber" Ted Kaczynski.

A rumour swirling online, prompted by a comment by a friend of Mr Loughner’s in an interview with the political website Mother Jones, suggests that his mother Amy Totman is Jewish.

But there have also been suggestions, including in a Department of Homeland Security memo, that Mr Loughner has links to an extremist and antisemitic organisation called American Renaissance.

Ms Giffords, an up-and-coming name in the Democratic Party and the state’s first Jewish representative, has been a vocal opponent of tightening immigration laws and during her re-election run last year was the subject of a heated Tea Party campaign to oust her.