Denmark was left stunned Wednesday by Donald Trump's decision to postpone a state visit after the government told the US president its autonomous territory Greenland was not for sale.

Danish Prime Minister Mette Frederiksen, who has called the idea of selling Greenland “absurd”, told reporters that she was “annoyed and surprised” at Trump's decision but insisted that US-Danish relations remain strong.

Trump tweeted on Tuesday that “based on Prime Minister Mette Frederiksen's comments, that she would have no interest in discussing the purchase of Greenland, I will be postponing our meeting scheduled in two weeks for another time.”

“The Prime Minister was able to save a great deal of expense and effort for both the United States and Denmark by being so direct.”

The decision confirmed just how interested Trump was in purchasing Greenland, an idea initially dismissed as a joke by some, but which the White House later insisted had a serious purpose because of its strategic location.

The territory — which is mostly covered in ice — has been essential to US defence since World War II.

'Show more respect'

The postponement has sparked strong reactions in Denmark.

“Reality transcends imagination... this man is unpredictable,” said Morten Ostergaard of the Social Liberal Party, which is part of the ruling coalition.

“For no reason, Trump assumes that (an autonomous) part of our country is for sale. Then insultingly cancels visit that everybody was preparing for,” tweeted Rasmus Jarlov, a member of the opposition Conservative Party.

“Are parts of the US for sale? Alaska? Please show more respect.”

Marc Jacobsen, a Greenland specialist at the University of Copenhagen, said Trump was acting like “an ignorant colonial overlord”.

“Trump's idea of purchasing Greenland is absurd, and it is absurd that he is now cancelling his state visit to Denmark when he knows that there is no chance Greenland will become the 51st state of America,” he told AFP.

Meanwhile, former US ambassador to Denmark Rufus Gifford wrote on Twitter: “He asks for an invitation from a great friend and ally. The Queen obliges invites him for a state visit. He declares the visit contingent on the great friend selling part of its territory to him This. Is. Not. Normal.”

Nonetheless, conservative newspaper Jyllands-Posten wrote that Trump's actions ultimately benefitted Denmark, highlighting Greenland's geopolitical value.

“Mette Frederiksen has been given the opportunity to emphasise that Greenland's big affairs are in fact decided in Copenhagen... strengthening Denmark's position in this great strategic game at stake over the Arctic,” it said.

Frederiksen herself said the US “remains one of Denmark's closest allies.”

“The developments in the Arctic region call for further cooperation between the US and Greenland, the Faroe Islands and Denmark,” she said on Wednesday, adding: “Our invitation for stronger cooperation on Arctic affairs still stands.”

Denmark's rejection of Trump's proposal “does not change the character of our good relations,” she insisted.

'A large real estate deal'

The Wall Street Journal first reported that Trump had expressed interest in the self-governing part of Denmark, asking advisors if it would be possible for the US to acquire the territory.

The president, a former real estate magnate, has been curious about the area's natural resources and geopolitical relevance, the paper said.

Asked on Sunday if he would consider trading a US territory for Greenland, Trump replied that “a lot of things could be done”.

“Essentially, it's a large real estate deal.” Denmark colonised the 772,000 square-mile (two-million square-kilometre) island in the 18th century. It is home to around 57,000 people, most of them from the indigenous Inuit community.

Greenland's foreign affairs ministry said on Friday that the island was ready to talk business — but was not for sale.

The territory is home to the US airbase Thule, crucial during the Cold War as a first line of monitoring against a potential Russian attack.

But the melting polar ice sheet is opening up potentially major shipping routes, and untapped reserves of oil, gas and minerals will become increasingly accessible, leading Russia and China to show mounting interest in the region.

As far back as 1867, the US State Department expressed interest in the island. And in 1946, President Harry S Truman offered $100 million in gold, or parts of Alaska, in exchange for Greenland.