"We are slowly normalizing production. We should be back to normal soon," Statoil spokeswoman Mari Dotterud said.
About 100,000 barrels of oil equivalent (boe) per day are normally extracted from the Norne field.
Production has been significantly reduced for a week because of severe storms raging along the coast of Troendelag in western Norway.
Norway is the world's third-largest oil exporter behind Saudi Arabia and Russia, producing some three million barrels a day.