"We believe that the fires were intentional because they occurred in the same period and a short distance from each other," Kenneth Berg of the Tønsberg police told NTB.
Police were notified about the mobile home fire at 3.30 on Wednesday morning, and then heard of the fire at a nearby four-story apartment building eight minutes later.
Police evacuated 41 people from the apartment building, 14 of whom were sent to hospital suffering smoke damage to their lungs.
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Tønsberg, around 60 miles outside Oslo, is regarded as Norway's oldest town.