Captain Flemming Madsen of the Danish Joint Arctic Command (JAC) told the Associated Press that the passengers and crew on the ship stranded in northwestern Greenland were doing fine and "all I can say is that they got a lifetime experience".
The scientific fishing vessel was scheduled to arrive later on Wednesday and would attempt when the conditions were right to pull the 100-metre-long and 18-metre-wide MV Ocean Explorer free.
The cruise ship ran aground above the Arctic Circle Monday in Alpefjord, which is in the Northeast Greenland National Park.
The park covers 972,000 square km, almost as much land as France and Spain combined, and approximately 80 per cent is permanently covered by an ice sheet, according to the Visit Greenland tourism board.
Alpefjord sits in a remote corner of Greenland, 240km away from the closest settlement, Ittoqqortoormiit, which itself is nearly 1400km from the capital Nuuk.
The Ocean Explorer's crew made two failed attempts to get the ship to float free on its own during high tide.
Australia-based Aurora Expeditions, which operates the ship, said the passengers and crew members were safe and well and that there was "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," it said.
Dozens of cruise ships sail along Greenland's coast every year so passengers can admire the picturesque mountainous landscape with fjords, musk oxen and the waterways packed with icebergs of different sizes and glaciers jutting out into the sea.
Madsen, of Denmark's JAC, said the passengers on the Ocean Explorer were "a mix" of tourists from Australia, New Zealand, the United Kingdom, the United States and South Korea.
Greenland is a semi-independent territory that is part of the Danish realm, as are the Faeroe Islands.
The people onboard "are in a difficult situation but, given the circumstances, the atmosphere on the ship is good, and everyone on board is doing well. There are no signs that the ship was seriously damaged by the grounding," the Joint Arctic Command said on Wednesday.
The weather in the region on Wednesday featured sun, a clear blue sky and a temperature of about 5C, according to the Danish Meteorological Institute.
The Ocean Explorer was built in 2021 and is owned by Copenhagen SunStone Ships, which is part of Denmark's SunStone Group.
It has an inverted bow, shaped like the one on a submarine.
It has 77 cabins, 151 passenger beds and 99 beds for crew, and several restaurants, according to the Sunstone Group website.
The JAC said there were other ships in the vicinity of the stranded cruise liner and "if the need arises, personnel from the Sirius Dog Sled Patrol can be at the accident site within an hour and a half".
On Tuesday, members of the Sirius Dog Sled Patrol, a Danish naval unit that conducts long-range reconnaissance and enforces Danish sovereignty in the Arctic wilderness, visited the passengers and explained the situation "which calmed them down as some were anxious," Madsen said.
The command, which was co-ordinating the operation to free the cruise ship, said the nearest Danish navy ship was more than 2000km away.
It was heading to the site and could be expected to reach the grounded ship as soon as Friday.
The primary mission of the JAC is to ensure Danish sovereignty by monitoring the area around the Faeroe Islands and Greenland, including the Arctic Ocean in the north.
with Reuters
