• A luxury cruise from South Africa to Argentina canceled its leg to Antarctica after an engine issue.
• Some passengers on the ship, the SH Diana, wanted more compensation to reflect their inconvenience.
• The cruise company's CEO said "a select few" staged a hunger strike, which was "counterproductive."

Some luxury cruise passengers have gone on hunger strike after their trip to Antarctica was canceled.

Swan Hellenic's 21-day cruise had to change course after a problem with one of the engines on the SH Diana, CEO Andrea Zito said in a Friday statement shared with Business Insider.

The Times of London reported that many passengers paid between £7,000 and £10,000 ($12,689) for the trip from Cape Town to Ushuaia, in southern Argentina.

The SH Diana is 409 feet long and has nine decks with space for 192 guests. Amenities include an outdoor pool, a spa, a library, and an expedition lab. On arrival, each cabin comes with a bottle of Champagne.

Zito said the SH Diana was supposed to stop in Antarctica for three and a half days, but the captain decided this was unsafe given the engine issue.

Instead, the ship is set to dock in Ushuaia on Saturday, leaving many passengers feeling upset after missing out on a key part of the trip.

"To go to Antarctica is a trip of a lifetime and this specific sailing made it achievable for many on board to do so as it's a repositioning sailing that had attractive deals," one passenger told The Times.

Swan Hellenic offered passengers a 50% cash refund, which Zito said was above the legal requirement of 30%. Alternatively, passengers could take a 65% "future cruise credit."

However, some people on board weren't pleased with the offer.

"A select few chose to stage a hunger strike in their protest," Zito said. He added that it was "rather counterproductive."

"We are working towards a swift end to this action."

The Times obtained pictures of some of these passengers with signs calling for a 100% cash refund.

"Swan Hellenic would like to reiterate that we deeply regret that we had to change the itinerary due to the technical problems with the propeller drive and we understand the disappointment of our guests who were looking forward to a taste of Antarctic experience," Zito said in the statement.

"We feel we have offered a very generous compensation package, beyond what is legally required," he added.

"Swan Hellenic always strive to go above and beyond our guest expectations and look forward to welcoming all our guests back on board future expeditions."