Police chased the man as he fled from his home in the Romanian capital, eventually arresting him in an outer suburb.
According to the Mediafax news agency, the man abused children of as young as ten years old after approaching them in the old town of Bucharest.
After he was arrested, Romanian police searched his home, finding several videos containing child pornography.
The arrest is part of a larger child pornography campaign mounted by Romania's Directorate for Investigating Organized Crime and Terrorism (DIICOT).
Ida Dahl Nilssen, a spokesman for Norway's criminal police service NCIS, said that they had not assisted the Romanian police in the case.
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"We have not received any request from the Romanian police. In cases investigated by another country's police, they will turn to us if they want assistance. But for the time being we have not been contacted," she said.
The Norwegian can now be held for 30 days pending a court hearing.