The shooter, a 32-year-old student from Rotterdam, wore a bulletproof vest as he shot and killed a 39-year-old woman and seriously injured her 14-year-old daughter, Police Chief Fred Westerbeke said on Thursday afternoon (early Thursday AEST).
The shooter then went to the nearby Erasmus Medical Centre where he shot and killed a 46-year-old man, a teacher at the academic hospital.
The suspect’s identity was not released and no motive was announced.
Earlier on Thursday, police had said a man wearing military clothing and carrying a handgun had opened fire in a classroom at the university hospital, wounding one person.
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Police said they did not believe any other shooters were involved.
The Erasmus Medical Centre appealed on social media for people not to go to the hospital.
There have been scores of small explosions at homes and businesses across Rotterdam this year, blamed on rival drug gangs.