Nuuk, Greenland - Greenland's newly elected Prime Minister Jens-Frederik Nielsen firmly rejected US President Donald Trump's threats to take control of the Arctic territory on Sunday, just days after taking office.

"Let me be clear: the US will not get Greenland. We do not belong to anyone else. We determine our own future," Nielsen wrote on Facebook.

Since taking office, Trump has repeatedly threatened to bring Greenland under US control, arguing that the resource-rich island of around 57,000 people is of strategic importance to the US.

He doubled down over the weekend, saying: "We'll get Greenland. Yeah, 100%."

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Trump told NBC said that there is a "good possibility it could be done without military force," but that he was not ruling anything out.

When asked what message an acquisition of Greenland would send to Russia and the rest of the world, he replied: "I don't really think about that. I don't really care."

Nielsen, for his part, advised a calm response to the threats. "We should not react out of fear. We should react with calm, dignity and cohesion," he said.

"That's how it was yesterday. That's how it is today. And that's how it will be in the future."

Nielsen's center-right Democrats won the parliamentary election on March 11 following an election campaign overshadowed by Trump's interest in Greenland, as well as the issue of full independence from Denmark.

Danish Prime Minister Mette Frederiksen plans to travel to Greenland on Wednesday with the aim of strengthening ties amid the geopolitical turmoil.