The gunman was among the dead at the Ridderhof mall in the town of Alphen aan den Rijn, about 13 miles southwest of Amsterdam, Sky News in Britain reported Saturday.
Police said they had identified the gunman and searched his house, DutchNews.nl reported. The shooter was a man who had previous dealings with police, investigators said, without releasing details.
Witnesses said the man appeared to be firing randomly and a motive wasn't immediately apparent. A resident near the shopping center said two bodies were visible lying on the ground outside the mall; more were thought to be inside.
The shopping center was evacuated and a safety zone around the mall was cordoned off. An unknown number of people were taken to area medical facilities.
A pet shop owner told Nos television he ducked into his store and pulled the shutters closed.
"There was a tremendous panic, everyone was running. I saw people lying on the ground," he said.
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