The 343 ft long Ocean Explorer ran aground on Monday in Alpefjord in a national park around 870 miles northeast of Greenland’s capital Nuuk.
The Danish Joint Arctic Command (JAC) said its nearest rescue vessel was around 1,200 nautical miles away at the time of the incident. This means it would not reach the grounded ship until Friday morning at the earliest.
No injuries have been reported, the JAC said.
Camilla Shouw Broholm, a spokeswoman for the JAC, said: “The Ocean Explorer ran aground Monday in the Alpefjord northeast of Greenland and has been unable to refloat itself.
“There are no injuries and the vessel has not sustained any damage. Our operations centre made contact with the ship. There are 206 passengers and crew on board.”
Commander Brian Jensen, the JAC’s head of operations, said: “A cruise ship in trouble in the national park is obviously a worry. The nearest help is far away, our units are far away, and the weather can be very unfavourable.
“However, in this specific situation, we do not see any immediate danger to human life or the environment, which is reassuring.”
The Ocean Explorer can accommodate up to 134 passengers and offers trips to “some of the most wild and remote destinations on the planet”, according to Aurora Expeditions.
The ship belongs to Ulstein Group in Ulsteinvik, southern Norway.
Authorities have been in contact with another cruise ship in the area and it had been asked to remain nearby to assist should the situation develop. The other cruise ship was not identified.
The grounded cruise ship might also get free on its own when the tide is high, Greenland television KNR reported. "Regardless, the most important thing for us is that everyone gets to safety," Jensen said.
Later Tuesday the Joint Arctic Command said on its Facebook page that the ship was still stuck despite the tide.
"There are still no reports that human life or the environment is in acute danger," Joint Arctic Command said.
The primary mission of the Joint Arctic Command is to ensure Danish sovereignty by monitoring the area around the Faeroe Islands and Greenland, two semi-independent territories that are part of the Danish realm.