Trump has insisted that Greenland needs to be brought under US control, arguing that the Danish autonomous territory is crucial for national security.
NATO and Greenland's government said on Monday that they intend to work on strengthening the defence of the Danish autonomous territory, hoping to dissuade US President Donald Trump from annexing the island.
On Sunday, Trump further stoked tensions by saying that the United States would take the territory "one way or the other," and poked fun at the island's defences, saying they consisted only of "two dog sleds."
Confronted with the prospect of annexation by force, Greenlandic Prime Minister Jens-Frederik Nielsen has placed his hopes in the US-led military alliance NATO.
"Our security and defence belong in NATO. That is a fundamental and firm line," Nielsen said in a social media post.
His government "will therefore work to ensure that the development of defence in and around Greenland takes place in close cooperation with NATO, in dialogue with our allies, including the United States, and in cooperation with Denmark," he added.
NATO chief Mark Rutte also said on Monday that the alliance was working on "the next steps" to bolster Arctic security.
Diplomats at NATO say that some alliance members are floating ideas, including possibly launching a new mission in the region.
Discussions are at an embryonic stage and there are no concrete proposals on the table so far, they say.
Trump has insisted that Greenland needs to be brought under US control, arguing that the Danish autonomous territory is crucial for national security.
Danish Prime Minister Mette Frederiksen has warned that if Washington followed through with an armed attack on Greenland it would spell the end of NATO.
In a bid to appease Washington, Copenhagen has invested heavily in security in the region, allocating some 90 billion kroner (€11 billion) in 2025.
Greenland, which is home to some 57,000 people, is vast with significant mineral resources, most of them untapped, and is considered strategically located.
Since World War II and during the Cold War, the island housed several US military bases but only one remains.
According to Rutte, Denmark would have no problem with a larger US military presence on the island.
Under a 1951 treaty, updated in 2004, the United States could simply notify Denmark if it wanted to send more troops.
Diplomatic front
Denmark is also working on the diplomatic front, with a meeting between Danish and Greenlandic representatives and US Secretary of State Marco Rubio expected this week.
According to US and Danish media reports, the meeting is set to take place Wednesday in Washington.
Danish Foreign Minister Lars Lokke Rasmussen on Monday posted a photo from a meeting with his Greenlandic counterpart Vivian Motzfeldt.
Denmark reportedly wants to present a united front with the leaders of the autonomous territory before the meeting with US representatives.
The Danish media reported last week on a tense videoconference between Danish lawmakers and their Greenlandic counterparts over how to negotiate with Washington.
Facing Trump's repeated threats, Nielsen said in his message on Monday: "I fully understand if there is unease."
In a statement published on Monday, the government in the capital, Nuuk, said it "cannot accept under any circumstance" a US takeover of Greenland.
A Danish colony until 1953, Greenland gained home rule 26 years later and is contemplating eventually loosening its ties with Denmark.
Polls show that Greenland's people strongly oppose a US takeover.
"We have been a colony for so many years. We are not ready to be a colony and colonised again," fisherman Julius Nielsen told the AFP news agency at the weekend.
And a bipartisan US congressional delegation will head to Copenhagen later this week in an attempt to show unity between the United States and Denmark, it emerged on Monday.
Senator Chris Coons will lead the trip of at least nine members of Congress and the group will be in Copenhagen on Friday and Saturday, according to a congressional aide familiar with the trip's planning.