The killings took place at a busy shopping centre in the town of Alphen aan den Rijn, about 25km (15 miles) south-west of Amsterdam.
The mayor of the town said the man opened fire with an automatic weapon and then shot himself.
The gunman came from the town, was known to police and "almost certainly operated alone", said a prosecutor.'Slaughter'
Kitty Nooy, from The Hague prosecutor's office, identified the man as 24-year-old Tristan van der Vlis, a member of a shooting club who had a permit to carry five weapons.
She said he was native Dutchman from Alphen who had had previous run-ins with the law, including an illegal weapons possession charge that was dropped.Continue reading the main story
People went over to them to help, thinking that they had fainted. When they understood that someone was firing shots, everyone started running”End Quote Mehdi Attha Witness Mayor Bas Eenhoorn called the incident "unprecedented" for the town of about 70,000 people.
He said four of the injured were in a critical condition and five had serious wounds.
Children were among the casualties, but officials say they are not prepared to say whether they were among the dead or the injured due to privacy reasons.
"It's hardly credible that our town could experience such slaughter, and on a day as beautiful as this," he said.
Most witnesses said the shooting lasted between 10 and 20 minutes, according to AFP news agency.
A shopkeeper in the Ridderhof centre said the gunman appeared to be shooting people at random.
"Initially, we thought it was fireworks," 37-year-old Mehdi Attha told AFP.
"Then the noises got closer and two people fell to the ground very close to me.
"People went over to them to help, thinking that they had fainted. When they understood that someone was firing shots, everyone started running," she added.
"I didn't see the shooter, I was just thinking about running."Evacuations
Another survivor, an elderly woman, described the killer as "big and dressed in camouflage pants".The incident happened at a busy shopping centre
"He moved about without haste, killing in cold blood," she told Dutch broadcaster NOS.
Ms Nooy said notes had been found in both Van der Vlis' house and car, but did not reveal their contents.
After the shooting, Mayor Eenhoorn ordered the evacuations of three other shopping centre in the town.
He did not give a reason for the decision, but Radio Netherlands reported that the note in the attacker's car had said he had planted explosives at the other malls.
Queen Beatrix and Prime Minister Mark Rutte issued statements expressing their shock and saying they sympathised with victims and families.
A resident told the BBC the shooting was unusual, despite being the second in the area this month.
"It's weird that something like this has happened in this neighbourhood. Usually nothing ever happens here. But this is the second shooting in two weeks," said Thomas Aantjes.
Two people were killed on 2 April in a shooting in the same district of the town. Officials have not made a link between the two incidents.
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