STORY: NOTE: VIDEO HAS BEEN EDITED TO HIGHLIGHT SUSPECT
Eyewitness video showed a man in a grey T-shirt and beige trousers firing a weapon
Abe, 67, was pronounced dead around five and a half hours after the shooting in the city of Nara. Police arrested a 41-year-old man and said the weapon was a homemade gun.
Nara police said the shooter, identified in the media as Tetsuya Yamagami, was a Nara resident and had worked at Japan's Maritime Self-Defence Forces for three years but now appeared to be unemployed. The police said they were investigating whether he had acted alone.
The suspect said he bore a grudge against a "specific organization" and believed Abe was part of it, and that his grudge was not about politics, the police said, adding it was not clear if the unnamed organization actually existed.