The weather front, dubbed Dagmar, is already believed to have wreaked more damage than Berit, the violent storm that battered Norway late last month.
Around 7,300 homes were still without electricity on Tuesday morning, while coastal areas were again pummeled by powerful winds.
“Winds have reached strong gale force for the most part and may develop into a full storm,” said meteorologist Anna Reistad in western Norway.
“The winds are then going to turn in a westerly direction and weaken to strong gales. It looks like the worst is over,” she added.
Several thousand residents in Årdal and Høyanger were cut off from the rest of the country following landslides and high winds in the early hours of Tuesday morning, while dozens of inhabitants in Høyanger and Jølster were evacuated from their homes as a result of the heightened landslide risk.
Strong winds are forecast to return to Norway on Wednesday, but these will mainly be confined to the Rogaland area.
Storm Dagmar brought hurricane force winds to many parts of the country on Christmas Day and Boxing Day. In Kråkenes, average wind speeds were clocked at 160.6 kilometres per hour.
National grid operator Statnett said around 100,000 people were left without electricity on Monday morning, and 7,300 households in Årdal and Høyanger were still without power on Tuesday morning.
With insurance firms already receiving more than 500 damage claims, Dagmar is expected to cost much more than Berit, which left a trail of destruction estimated at 275 million kroner (€46 million).