Expedition cruise ship Ocean Explorer ran aground in a remote part of eastern Greenland with 206 passengers and crew on board.
Authorities were said to be in contact with the AE Expeditions vessel following the incident on Tuesday.
The ship was sailing in the Alpefjord in the southeast part of the Northeast Greenland National Park, the world’s largest and most northerly national park.
A branch of Joint Arctic Command (JAC), the Danish military responsible for patrolling Greenland, was informed that the ship was unable to free itself.
The JAC, which provided details on its Facebook page, said there had been no reports of injuries and no immediately risk of harm to those on board.
However, its nearest ship was inspection vessel Knud Rasmussen positioned 1,200 nautical miles away at the time of the incident, meaning that it could take until Friday morning local time to reach Ocean Explorer.
JAC head of operations Commander Brian Jensen was reported by the Telegraph as saying: “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.”
Another cruise ship, reported to be Silversea Expeditions’ Silver Endeavor, had been requested to stay in the area to offer assistance as required.
Jensen was also said: “They can either try to get free on their own when it gets high tide, they can get help from a nearby cruise ship, they can get help from Knud Rasmussen, or they can get help from one of our partners.
“Either way, the most important thing is that everyone gets to safety.”
Australian cruise operator Aurora Expeditions said in a statement: “The MV Ocean Explorer ran aground during its voyage, in Alpefjord, Greenland on Tuesday.
“All passengers, the expedition team and crew onboard are safe and well. Importantly, there is no immediate danger to themselves, the vessel, or the surrounding environment.
“We are actively engaged in efforts to free the MV Ocean Explorer from its grounding. Our foremost commitment is to ensure the vessel’s recovery without compromising safety.
“We have also secured the support of other vessels in the vicinity should their assistance become necessary.
“As we continue to gather more information and progress in our efforts, we will provide further updates.”
The 134-passenger Ocean Explorer is sister ship to AE’s Greg Mortimore and in the same Infinity class as the company’s latest vessel Sylvia Earle.
“The Infinity-class has set new standards for expedition cruise vessels and received numerous awards for its eco-friendly design and construction,” the AE Expeditions website states.