"Our first priority was for the safety and wellbeing of our passengers and our crew, and in close cooperation with the Norwegian Coast Guard, the captain chose to evacuate all guests from the vessel by helicopter", the Viking spokesman added, noting that the "evacuation is proceeding with all necessary caution" despite the injuries.
The Norwegian Maritime Rescue Services reported mayday calls from the Viking Sky as it was drifting towards shore.
Rescue service spokesman Einar Knudsen told the Reuters news agency that rescuing all passengers "will take a long time".
Several vessels and five helicopters were deployed to help rescue passengers.
By 4:30 pm (1430 GMT) 100 people had been evacuated, with four helicopters involved in the airlift. Norwegian media reported gusts up to 38 knots (43 mph) and waves over 8 meters (26 feet) in an area known for its rough, frigid waters. "It has dropped anchor and one of its engines is working", said a rescue centre spokesman, Borghild Eldoen.More news: The college-admissions scandal should make everyone furious
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Passengers were hoisted one by one from the deck of the ship and airlifted to a village located to the north of the town of Molde on the Norwegian west coast.
Authorities told NRK that a strong storm with high waves was preventing rescue workers from using life boats or tug boats to take passengers ashore.
"It's a demanding exercise, because they [passengers] have to hang in the air under a helicopter and there's a very, very strong wind", Odd Roar Lange, a witness at the site, told NRK.
Video footage from on board the cruise ship Viking Sky shows furniture rolling around and parts of the ceiling collapsing.