Nuuk, Greenland - Greenland's prime minister on Wednesday hit back at President Donald Trump's threat to seize the Arctic territory "one way or the other," insisting that islanders did not see their future with the US or even Denmark.

Mute Egede rejected Trump's expansionist ambitions to annex the sparsely populated but mineral-rich and strategically placed island, in his address to Congress Tuesday.

"We don't want to be Americans, or Danes either. We are Greenlanders. The Americans and their leader must understand that," Egede wrote in a Facebook post.

"We are not for sale and can't just be taken. Our future is decided by us in Greenland," he said, six days before the island's legislative elections where the longstanding question of independence tops the agenda.

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Trump offered only passing lines on world affairs in his speech, focusing on his domestic goals like rounding up undocumented immigrants and slashing government spending.

But he repeated his aspirations to take Greenland and claimed an initial victory on retaking control of the Panama Canal.

Trump said he had a message for the "incredible people" of Greenland. "We strongly support your right to determine your own future, and if you choose, we welcome you into the United States of America," he added.

But he made clear he would not give up if persuasion fails, saying: "One way or the other we're going to get it.

"We will keep you safe, we will make you rich, and together, we will take Greenland to heights like you have never thought possible before."

Denmark, of which self-governing Greenland is part, has also repeatedly rejected Trump's obsession.

In Copenhagen, Danish Defense Minister Troels Lund Poulsen told public broadcaster DR that US annexation of Greenland "won't happen."

"The direction that Greenland wants to take will be decided by Greenlanders," he said.

Danish Foreign Minister Lars Lokke Rasmussen called for cool heads to prevail.

"I think everyone, including us, should be cautious about having all kinds of opinions about the future" of Greenland, he told Danish television TV2.