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Viking has a fleet of 79 vessels offering scenic cruising on rivers and oceans around the world, including in New Zealand.
The announcement was made today in a video and a letter sent from Viking chairman Torstein Hagen to passengers currently booked.
The 23-year-old company carries about 500,000 guests each year and has 10,000 staff.
''I am sure you recognise that Covid-19 has made travel exceedingly complicated,'' said Hagen.
''The situation has now become such that operating as a travel company involves significant risks of quarantines or medical detentions, which could diminish the travel experiences for which our guests have been planning.''
An increasing number of ports, including Venice, Monte Carlo and Bergen, have temporarily closed to cruise ships; major attractions such as the Vatican and other museums have been closed; and some countries are imposing restrictions on public gatherings and visitors.
Recently one of its river cruise guests in Southeast Asia was exposed to Covid-19 while in transit on an ]airline. While this guest was not exhibiting symptoms, she has been placed in quarantine. Separately, the remaining 28 guests will also be quarantined.
Hagen said that as a private company with strong finances, it did not have to worry about quarterly profit expectations.
''That flexibility allows us the ability to do what is best for our guests and our employees, as we have always done.''
He said he had made the ''difficult'' decision to temporarily suspend operations of the firm's river and ocean vessels embarking from March 12 to April 30.
At that time it was believed Viking would be in a better place to provide the experiences guests expect and deserve.
''This is a decision we made with a heavy heart, but with present circumstances what they are, we are unable to deliver the high-quality Viking experience for which we are known.''
Guests could take a cruise at a later date.
Viking's decision is the latest blow to the embattled cruise industry which generates $200b in economic activity. Governments around the world have warned passengers, especially those with underlying health conditions, to reconsider travel on cruises.