The Danish military's Joint Arctic Command (JAC) said Tuesday's tide had failed to lift the 104-metre (341-foot) 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 on Wednesday.
The passengers and crew remained safe on board, Australian cruise operator Aurora Expeditions said.
"There is no immediate danger to themselves, the vessel, or the surrounding environment," Sydney-based Aurora said in a statement.
"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."
The Bahamas-flagged MV Ocean Explorer vessel is purpose-built for accessing the world's most remote locations.
The ship ran aground on Monday while touring the Alpefjord National Park, some 1400km 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.Â
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