A source close to the investigation told the Washington Post that 22-year-old Jared Loughner was researching lethal injections, solitary confinement and political assassinations just before the Jan. 8 shooting. The gunman killed six people and injured 13 others in a rampage outside a supermarket.
The Washington Post reports the FBI found the internet searches on the suspect's computer.
Meantime, Ariz. Congresswoman Gabrielle Giffords was moved Wednesday out of intensive care at a hospital in Houston, Texas. Her condition has improved from serious to good.
Doctors said she will have a valve inserted into her breathing tube to help her talk. Giffords began physical, occupational and speech therapy just hours after she was transferred.
The Associated Press contributed to this report.