Norwegian public broadcaster NRK said the Viking Sky's evacuation was likely to be a slow and risky process, as passengers needed to be hoisted from the cruise ship to the five available helicopters one by one.
Another passenger told Norwegian television she "never experienced anything so scary".
Eight individuals were reported to have sustained minor injuries from the cruise ship, while a 90-year-old man and his spouse had been severely injured, the AP reported.
"These people can not be lifted from the ship because of the rough seas", he said.
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The cruise ship Viking Sky lays at anchor in heavy seas, after it sent out a Mayday signal.
Fisherman Jan Erik Fiskerstrand, whose boat was one of the first to come to help MV Viking Sky, told Aftenposten newspaper, "it was just minutes before this could have gone really wrong".
The ship named Viking Sky was drifting towards land when it let out the distress signal.
A Norwegian cruise ship is evacuating passengers after experiencing engine problems in rough weather.
The majority of the cruise ship passengers were reportedly British and American tourists.
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The cruise ship had been en route from Tromso to Stavanger.
Another video, shared by passenger David Hernandez, captured water running underneath his feet as he waited for evacuation.
By 9:00 pm (2000 GMT) 136 people had been evacuated, with each helicopter able to take 15-20 people per airlift.
Norwegian authorities said late Saturday that the evacuation would proceed all through the night into Sunday.
Unfortunately for the roughly 1,300 passengers and crew stuck aboard the vessel, the evacuation is expected to be a slow and harrowing process, as each passenger needs to be hoisted from the ship aboard one of five rescue helicopters. They were forced to divert some resources when a nearby freight vessel lost engine power, putting that ship's crew in danger, rescue center officials said.
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The Viking Sky ship, owned by Viking Ocean Cruises, was built in 2017 and can hold 930 guests, according to the company's website.