Shooting rampage accused wrote 'Die, bitch' in home message

Investigators believe Jared Loughner's handwritten message was a reference to Ms Giffords, Pima County Chief Rick Kastigar said.

It was found in a safe alongside other ones, including "I planned ahead," "My assassination" and the name "Giffords".

Authorities are piecing together the events in the hours leading up to the Saturday shooting that killed six people and injured 14 others, including Ms Giffords. Loughner took a taxi cab to the supermarket where the three-term Democrat was holding a meeting to hear the concerns of her constituents. Among those killed were a federal judge and a nine-year-old girl.

A memorial service for the murdered victims was held in Tucson on Tuesday night. President Barack Obama and his wife Michelle was joining the mourners in Arizona and give a speech honouring those killed and those who overcame the gunman to prevent more being shot.

Loughner's parents, silent and holed up in their home since the shooting spree, have apologised.

"There are no words that can possibly express how we feel," Randy and Amy Loughner wrote in a statement handed to reporters waiting outside their house. "We wish that there were, so we could make you feel better. We don't understand why this happened.

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

The apparent target of their son's attack, Ms Giffords, 40, is now able to breathe on her own at an intensive care unit.

While doctors are confident of her survival from the head wound, caused when a bullet passed through her skull down the left side of her brain, they have stressed she is in for a long recovery.

Assurances of her survival came as the political fallout over the shooting continued. Right-wing US politician Sarah Palin has posted a nearly eight-minute video on her Facebook page condemning those who blame vitriolic political campaigning for the massacre.

She has been criticised for an online campaign map that targeted the district of shot congresswoman Gabrielle Giffords with the cross-hairs of a gunsight.

In the video, the 2008 Republican vice presidential candidate said vigorous debates are a cherished tradition but said after an election both sides find common ground.

She said journalists should not manufacture what she called a "blood libel" that incites hatred.