US President Donald Trump yesterday called off a visit to Denmark scheduled for early September after the country's prime minister rebuffed his idea of purchasing Greenland.

"Denmark is a very special country with incredible people, but 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 said in a post on Twitter.

"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. I thank her for that and look forward to rescheduling sometime in the future."

A White House official said Trump had dropped the Sept 2-3 stop in Denmark, a Nato ally. Trump had been due to discuss the Arctic in meetings in Copenhagen with Frederiksen, who took office in June, and Prime Minister Kim Kielsen of Greenland.

He is due to visit Poland on Aug 31.

Frederiksen said on Sunday the idea of selling Greenland to the United States was absurd after an economic adviser to Trump confirmed US interest in buying the island.

"Greenland is not for sale. Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously," Frederiksen told the newspaper Sermitsiaq during a visit to Greenland.

Trump confirmed to reporters on Sunday that he had recently discussed the possibility of buying Greenland, an autonomous Danish territory, although he said such a move was not an immediate priority.

"The concept came up and ... strategically it's interesting," Trump told reporters in Morristown, New Jersey.

A defence treaty between Denmark and the United States dating back to 1951 gives the US military rights over the Thule Air Base in northern Greenland.

Trump's interest in buying Greenland has been met with incredulity and humour. Lars Lokke Rasmussen, who recently stepped down as Danish prime minister, tweeted last week: "It must be an April Fool’s Day joke."

On Monday, Trump retweeted an image of a golden Trump tower looming over a cluster of houses on the Arctic island, and wrote: "I promise not to do this to Greenland!"

- Reuters