A man charged with trying to assassinate a US congresswoman in a shooting that left six people dead and more than a dozen wounded has appeared in federal court in Phoenix, Arizona.

Jared Loughner, 22, faces several charges over the attack on Saturday.

Loughner walked into the courtroom wearing handcuffs and in a prison uniform, with a cut on the right side of his head.

During the 13-minute hearing, he said very little, only periodically leaning forward to speak into a microphone.

Loughner, who did not enter a plea, confirmed his identity and had an attorney appointed to defend him.

When asked, he said he understood that he could get life in prison or the death penalty for allegedly killing federal Judge John Roll on Saturday in Tucson, Arizona.

Representative Gabrielle Giffords, who was shot in the head, remains in a critical condition but doctors say the swelling in her brain has stabilised.

Among the dead were a nine-year-old girl and a federal judge.

President Barack Obama, who led the US in a silent tribute from the South Lawn of the White House on Monday morning, said a priority for the nation was "making sure we are joining together, pulling together as a country".

The president will travel to Arizona on Wednesday to attend a memorial service for the victims of the Arizona shooting, administration officials said.