Dutch authorities had rung alarm bells about the "psychotic behaviour" of a man suspected of a shooting and arson rampage through Rotterdam that claimed three lives, according to local media Friday.

The Public Prosecution Service had written earlier in the year to the Erasmus university hospital about the medical student suspected of shooting dead his neighbour, her 14-year-old daughter, and a teacher at the hospital.

The man, named locally as Fouad L., displayed "worrying" and "psychotic" behaviour, including lying half-naked on a pile of leaves in his garden and laughing maniacally, prosecutors told the university in an email confirmed to be authentic by public broadcaster NOS.

Authorities had also examined the 32-year-old's phone and found images of people being stabbed, along with far-right propaganda, according to the email.

"I assume this will influence your decision as to whether he is eligible for the basic medical diploma," prosecutors wrote in the email.

The suspect, now in custody, first stormed into his neighbour's house, shooting dead a 39-year-old woman and severely wounding her 14-year-old daughter, who later died of her injuries.

He set fire to this house and then moved to the hospital, bursting into a classroom and shooting dead a 43-year-old teacher. Police had initially said the teacher was 46 before correcting the age.

Dressed in combat gear and wearing a bulletproof vest, the gunman went to the main wing of the hospital and set the building ablaze, sparking panic as medical staff tried to evacuate patients, some in wheelchairs and stretchers.

Police said the suspect was cooperating with their enquiry and have not yet given a motive.

The suspect had been convicted for animal cruelty after abusing his pet rabbit and prosecutors said in their letter that his acts had been filmed by a neighbour. It was not yet clear whether the neighbour was the person he shot.

He is thought to have held a deep grudge against the hospital, although it is not known whether the facility had acted on the warning from prosecutors.

Police said that he had acted alone and that the killings were "targeted", not random.