Local media say up to 19 people have died and as many as 50 are injured.
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Four of those injured are reported to be in a serious condition.
Kanagawa Prefecture is located about 20 miles from Tokyo.
According to local sources, the man broke into a building which was used as a facility for disabled people.
Police swarmed the scene after an employee of the facility called for help about 2:30 a.m. Tuesday, NHK reports.
In the developed world, Japan has one of the lowest rates of violent crime.
In Japan, mass stabbing incidents are unusual but do happen.
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Armed police encircled the centre and arrested a man in his 20s on suspicion of murder.
