Monday's shooter, identified as a 24-year-old Swiss national of Ghanaian origin known to the police, had stabbed a Swiss national to death just a day earlier at a Zurich playground, cantonal police Christiane Lentjes Meili told reporters.
"We don't know anything about the motives," she said, adding that the shooter appeared to be deeply interested in "the occult".
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"Corresponding symbols have been found at his home," she said.
According to investigators, there is no indication that the shooter had any links to terrorism or far-right movements.
Lentjes Meili said the man had a legal permit for the gun he used in the shooting, and that it remained unclear if he was suffering from mental problems.
Dressed in black, the shooter burst into the Islamic Centre in central Zurich around 5:30 pm (1630 GMT) on Monday and started shooting.
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He injured three worshippers, aged 30, 35 and 56.
Two were seriously hurt, but Lentjes Meili told reporters that after surgery, all three men were now in stable condition.
Shortly afterwards, a body was found a few hundred metres (yards) from the scene on a river bank under a bridge.
Lentjes Meili confirmed Tuesday that the body belonged to the shooter, and that he appeared to have turned his gun on himself after his rampage.
Investigators believe that the shooter lived alone.
He had been working at an undisclosed shop, but had quit his job last Friday, Lentjes Meili said.
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