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Public broadcaster NHK said police had taken a 41-year-old man into custody who allegedly shouted "Die!" as he poured what appeared to be gasoline around the three-story building of Kyoto Animation shortly after 10 a.m. (0100 GMT).
The man was injured and was being treated at a hospital, preventing police from questioning him, NHK said.
TV footage showed white and black smoke billowing out of the windows of the studio's building. The studio produces popular series such as the "Sound! Euphonium", and its "Free! Road to the World - The Dream" movie is due for release this month.
The casualties included seven confirmed dead, six with no vital signs, and another 10 or so people found unconscious, a Kyoto city fire department official told Reuters.
Another 36 have been injured, 10 of them seriously, he said.
"I heard the sound of fire engines and stepped outside my house, and saw big flames spewing out of the building," NHK quoted a 16-year-old boy as saying.
"Fire department officials were trying to rescue the injured in a nearby park but it seemed like there weren't enough of them," he told NHK.
The fire department official said earlier that some 30 people believed to have been in the building at the time could not be reached. Some or all of the 10 or so people later found unconscious on the top floor and the staircase leading to the rooftop may be included in that tally, he said.
Kyoto police declined to comment.
Violent crime is relatively rare in Japan but occasional high-profile incidents have shocked the nation.
Less than two months ago, a knife-wielding man slashed at a group of schoolgirls at a bus stop in Kawasaki, a city just south of Tokyo, killing one girl and the father of another student, while injuring more than a dozen other children.
In 2016, a man armed with a knife broke into a facility for the disabled in a small town near Tokyo and killed 19 patients in their sleep.