According to Dutch police, the man who was in a tram in Utrecht pulled out a gun and started shooting people.
In neighboring Germany, police said they stepped up surveillance of the Dutch border, watching not only major highways but also minor crossings and train routes.
"We can not exclude a terrorist motive", the head of the Dutch national counterterrorism service, Dutch National Coordinator for Security and Counterterrorism Pieter-Jaap Aalbersberg told a brief news conference before rushing off for a crisis meeting.
Several people have been injured in a shooting incident on a tram in Utrecht, police have confirmed, but few details are yet available.
Emergency services flooded the area around a busy traffic intersection in the west of the city where the shooting took place.
Prime Minister Mark Rutte said he was "deeply concerned" and an emergency meeting between ministers is expected to take place later on Monday. The country's head of counter-terrorism said the shooting "appears to be a terrorist attack".
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Photos and footage show a large number of armed police surrounding the building in the university city.
Utrecht police said on Monday that they were considering the possibility of a "terrorist motive".
Omar Rahhou, who said his parents lived on a street cordoned off by police, said: "It's frightening that something like this can happen so close to home".
The Netherlands' fourth-largest city was on lockdown. Police spokesman Joost Lanshage, citing the investigation, declined to comment on the reports that Gokmen had a criminal record.
Utrecht is in the Netherlands' central region, about 20 miles southeast of Amsterdam.
The shooting comes just days after the deadly attack on two mosques in New Zealand, in which 50 people were killed.