Federal law-enforcement authorities intensified their investigation Friday into suspected Pentagon shooter John Patrick Bedell, whose erratic behavior prompted his parents to contact the police in the months before the attack that left two police officers wounded.

Mr. Bedell, 36 years old, died late Thursday night from the wounds he suffered after opening fire at police officers guarding the Pentagon earlier that evening. Pentagon police officials said Mr. Bedell, who was carrying two semi-automatic handguns and several magazines of ammunition, was trying to enter the fortified Defense Department headquarters. Authorities believe Mr. Bedell, who harbored—and had expressed—anger toward the federal government, acted alone.

Officials from the Federal Bureau of Investigation and the Pentagon Force Protection Agency said Mr. Bedell emerged from the Pentagon subway station Thursday evening and made his way to a nearby guard post. When officers asked for his identification, Mr. Bedell, who was wearing a white button-down shirt and blazer, pulled out a pistol and started shooting.

The investigators said Mr. Bedell, who had studied physics and engineering, drove to Washington from his parents' home in Hollister, Calif., in the days before the assault. Mr. Bedell's 1998 green Toyota Avalon was recovered from a garage at the Pentagon City Mall hours after the attack. Additional ammunition was found in the car, authorities said.

Mr. Bedell's parents reached out to law-enforcement officials after growing concerned about their son's mental health. According to police in San Benito County, the Bedells filed a missing-persons report about their son on Jan. 4 after not hearing from him for several days.