A luxury cruise ship carrying 206 people remained stuck in a remote Greenland location on Wednesday after running aground earlier this week, the vessel's operator and rescue services said.

The Danish military's Joint Arctic Command (JAC) said Tuesday's tide had failed to lift the 104-metre Ocean Explorer enough to free it.

"The tide that came in during the day, local time, did not provide the desired help to sail on," the JAC said in a statement.

Australian cruise operator Aurora Expeditions said that the passengers and crew remained safe on board.

"There is no immediate danger to themselves, the vessel or the surrounding environment," Sydney-based Aurora said in a statement.

The ship ran aground on Monday while touring the Alpefjord national park, some 1,400 kilometers northeast of Greenland's capital Nuuk, where the nearest rescue vessel is still days away.

Photos taken by a Danish air force plane on Tuesday showed the Ocean Explorer sitting upright in calm waters with the sun shining.

The JAC said it remained in contact with nearby ships to see whether they would be able to help free the Ocean Explorer.

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.

(With input from Reuters)