A fishing trawler’s attempt to free a luxury cruise ship that ran aground two days ago in a remote part of Greenland has failed, leaving 206 passengers (including 90 Australians) still stranded.

The Ocean Explorer has since Monday been stuck in mud and silt in the Alpefjord national park, 1400 kilometres north-east of Greenland’s capital Nuuk.

A trawler tried to pull the cruise ship free at the high tide on Thursday (AEST) but could not, the Danish military’s Joint Arctic Command said.

Armed forces personnel stationed in Greenland have inspected the Ocean Explorer and spoken to those on board, concluding that they were in good condition.

“The crew and passengers are in a difficult situation but under the circumstances the atmosphere on the ship is good and everyone on board is doing well,” the JAC said.

The Danish navy’s Knud Rasmussen patrol vessel was expected to arrive at the Alpefjord site late on Friday (local time), the JAC said.

“If everything goes well, they will help the ship get out of this emergency that they’re in at this moment. But it depends on how everything looks when they arrive on Friday so we need to see how it goes,” a JAC spokesperson said.

The Sydney Morning Herald reports there are cases of COVID on board, but one retired Sydney couple said passengers were “in good spirits”.

“It’s a little bit frustrating, but we are in a beautiful part of the world. We’re sitting right near the glacier when we open our window,” Steven Fraser and Gina Hill told the news outlet.

The Ocean Explorer is designed to travel to remote destinations. Photo: Aurora Expeditions website.

The passengers and crew remained safe on board, Australian cruise operator Aurora Expeditions said earlier.

“There is no immediate danger to themselves, the vessel or the surrounding environment,” said the statement.

Captain Flemming Madsen, of the JAC, said passengers and crew on the ship were doing fine and “all I can say is that they got a lifetime experience”.

Captain Madsen said those on the Ocean Explorer were “a mix” of tourists from Australia, New Zealand, Britain, the US and South Korea.

The Ocean Explorer has 77 cabins, 151 passenger beds and 99 beds for crew, and several restaurants, according to the Sunstone Group website.

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Photos taken by the Danish military showed the Ocean Explorer sitting upright in calm waters with the sun shining.

Greenland, a semi-sovereign territory of Denmark in the North Atlantic Ocean with a population of just 57,000, attracts tourists with its rugged landscape and a vast ice cap that covers much of the island.