"As the investigation goes on, there may well be additional charges that will be filed," Robert Mueller, director of the Federal Bureau of Investigation, told reporters in Tucson.
Loughner, 22, was detained Saturday by bystanders outside a grocery store outside of Tucson after he shot at Giffords with a semi-automatic pistol. He fired 31 shots, injuring Giffords and 14 others, and killing six people, including a federal judge and a nine-year-old girl.
In a search of Loughner’s home, where he lived with his family, police found an envelope in a safe with hand-written notes saying "I planned ahead," "My assassination" and "Giffords".
Investigators have not spoken about Loughner’s motives or mental state.
Authorities said he was expelled last year from a community college.
The FBI is investigating whether he is the same person who posted a rambling manifesto posted online accusing the government of mind control and demanding a new currency.
Doctors said it was too early to say how long it will take Giffords to recover from the bullet wounds to her head. She remains in an induced coma.
Doctors voiced optimism, saying they are very encouraged by her ability to communicate, as the bullet did not go through both hemispheres of her brain.
“I am cautiously optimistic," said Michael Lemole, the neurosurgeon who operated on her at University Medical Centre. “Congresswoman Giffords is able to communicate with us... following simple commands,” he said, adding that, “brain swelling at any time can take a turn for the worse.”