Democrats Party leader Jens-Frederik Nielsen took to social media on Sunday to fire back at mounting pressure on Greenland from the Trump administration.
"President Trump says that the United States is getting Greenland. Let me be clear: The United States won't get that. We do not belong to anyone else. We determine our own future," Nielsen said on Facebook.
"We must not react with fear. We must respond with calm, dignity and unity."
Trump on Saturday told NBC News he "absolutely" had real conversations about annexing the autonomous Danish territory.
"We'll get Greenland. Yeah, 100 per cent," Trump told NBC.
During a visit to a US military base in the north of Greenland on Friday, US Vice President JD Vance accused Denmark of not doing a good job of keeping the island safe and suggested America would better protect the strategically located island.
Former Danish prime minister Helle Thorning-Schmidt pointed out that the US had 17 military bases in Greenland during the Second World War but had scaled down its presence.
She said the Americans have huge access to Greenland under a 1951 treaty with Denmark.
"The Americans have basically scaled back... The Americans have also taken a peace dividend in Greenland," she told CNN.
"Are we in such a new situation so we all have to scale up in Greenland?"
Denmark's Foreign Minister Lars Løkke Rasmussenon scolded the Trump administration for its "tone" in criticising Denmark.
Denmark has already decided to invest $US1 billion ($A1.6 billion) in Arctic security, Rasmussen said.
Greenlanders went to the polls earlier in March, and a broad four-party coalition government, led by Nielsen, was announced on Friday, hours before Vance's visit.
Danish Prime Minister Mette Frederiksen will visit Greenland this week to discuss co-operation with the territory and have talks with Nielsen.
Hundreds of protesters demonstrated on Saturday outside the US Embassy in Copenhagen and there have also been anti-US rallies in Nuuk earlier this month.
Greenland is an autonomous Danish territory of 57,000 people which has had self-rule since 2009.
Between the Arctic and Atlantic oceans, the world's biggest island has been controlled by Denmark for about 300 years.
It governs its own domestic affairs but its foreign and defence policies are formulated in Copenhagen.
