This combination of pictures created shows Denmark's Prime Minister Mette Frederiksen and US President Donald Trump. Tobias Schwarz and Nicholas Kamm / AFP

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.

The Danish Royal House expressed "surprise" at Trump's cancellation while commentators accused Trump of acting like a "colonial overlord".

"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," Trump tweeted on Tuesday.

"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." His comments came two days after Frederiksen had rejected the president's proposal to possibly buy Greenland as "absurd".

The decision confirms just how interested he 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 has been essential to US defence since World War II.

Prime Minister Frederiksen was due to hold a press conference at 1300 GMT on Wednesday.

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 said.

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 daily 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.

Agence France-Presse