Police spokeswoman Dianne van Gameren said the victims were "primary school age" and some of them came from the same family. Their identities were not released.
The accident happened in the southern town of Oss, 100 kilometers (62 miles) southeast of Amsterdam, at a rail crossing close to one of its railway stations. The crossing has warning lights and red-and-white barriers to keep pedestrians off the tracks when trains pass.
Police said the electric vehicle belonged to a children's day care center and was taking children to school when the collision happened.
The vehicle involved was an electric cargo bike, which has a large wooden or plastic box mounted to the frame in front of the rider. They were formerly used for transporting goods but are now very popular among Dutch parents for carrying young children. The driver stands on a platform behind a large container and steers using bicycle-like handlebars.
The two critically injured victims, a child and the woman operating the vehicle, were taken to a local hospital.
ProRail, the company responsible for rail infrastructure in the Netherlands, said the cause of the collision is under investigation.
"This is a very dark day, terrible for the next of kin and those involved," said ProRail CEO Pier Eringa. "There are no words to describe this."
Eringa said initial investigations suggested that the barriers at the crossing were working correctly at the time of the accident.
"Our thoughts are with the families who lost their children in the terrible accident in Oss," a visibly upset Dutch Queen Maxima told reporters during a visit to the northern region of Friesland.
Oss Mayor Wobine Buijs-Glaudemans offered condolences to "the families, the school, the day care center and everybody else involved."
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