WASHINGTON — The 66-year-old gunman who opened fire one week ago on members of Congress at a Northern Virginia ball field most likely acted spontaneously, the F.B.I. said Wednesday, describing his increasing desperation in recent weeks as he moved halfway across the country, unemployed, living in a van and facing a crumbling marriage and anger management problems.

Investigators cautioned that they had not settled on a motive for James T. Hodgkinson of Belleville, Ill., who was killed in an early morning firefight with police officers on June 14. They said that he had no links to terrorism and that he acted alone. But a lengthy statement from the F.B.I. provided the most complete picture to date of Mr. Hodgkinson’s time in Virginia, where he moved in the weeks before the shooting.

“He was struggling in all kinds of different ways,” Timothy R. Slater, a senior F.B.I. agent at the Washington Field Office, said during a news conference. “I think he was struggling in a lot of aspects of his life.”

Representative Steve Scalise of Louisiana, one of the shooting victims, improved to fair condition and was starting rehabilitation, MedStar Washington Hospital Center officials said Wednesday. They had said previously that Mr. Scalise, the No. 3 Republican in the House, had been at “imminent risk of death.”