"We are searching for the last three. We have rescued 13 of the 16 people aboard the plane and most of them are in good condition," Terje Langaas, a spokesman for Norway's rescue centre, told public broadcaster NRK.
Police officials earlier said passengers were being treated at the airport and transported to a nearby hospital.
The accident occurred around 7.37am local time in Stord, an island south of Bergen on Norway's western coast.
The plane was chartered by oil services firm Aker Stord, part of offshore engineering group Aker Kvaerner.
The Atlantic Airways plane from Denmark's self-governing Faroe Islands in the North Sea was making a stopover between Norway's offshore oil capital of Stavanger and the town of Molde, further up the country's western coast, Aker Stord said.
Molde is the base for the huge Ormen Lange gas field, which will soon supply Britain with 20 per cent of its gas needs.
Public broadcaster NRK aired voices of anonymous witnesses, who talked of a loud boom, a fireball and billowing smoke.
Pictures from the site showing a huge smoke chimney above still burning debris filled Internet pages of Norwegian tabloids.