The US president had floated the idea of buying Greenland from Denmark - AP

Donald Trump has scrapped his meeting with the Danish prime minister after his suggestion of buying Greenland was categorically rejected.

The US president, who had floated the idea of buying the semi-autonomous Danish territory in the Arctic, had been set to visit Denmark early next month.

But after Denmark's Prime Minister Mette Frederiksen called Mr Trump's musing "an absurd discussion", he decided to postpone the meeting.

"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," he tweeted.

"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!"

After discussion of the purchase was first reported on Thursday, Mr Trump confirmed his interest in buying the territory on Sunday but said it was not a priority for his administration.

"Strategically it's interesting and we'd be interested, but we'll talk to (Denmark) a little bit," he told reporters, adding that he viewed it as a "large real estate deal."

Calling the proposition "an absurd discussion", Ms Frederiksen said: "Greenland is not Danish. Greenland is Greenlandic. I persistently hope that this is not something that is seriously meant."

She said the Arctic, with resources that Russia and others could exploit for commercial gain, "is becoming increasingly important to the entire world community."

Danish Prime Minister Mette Frederiksen and Greenland Premier Kim Kielsen on Monday Credit: Rex

Ms Frederiksen, who became prime minister June 27, was on a two-day trip to Greenland before traveling to nearby Iceland for a meeting of the Nordic prime ministers this week.

"Thankfully, the time where you buy and sell other countries and populations is over. Let's leave it there. Jokes aside, we will of course love to have an even closer strategic relationship with the United States," Ms Frederiksen said.

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At a meeting on Tuesday in Iceland of the Nordic government leaders, Greenland Premier Kim Kielsen told The Associated Press that Mr Trump's idea "is not something to joke about."

On Monday, Mr Trump jokingly promised that he would not build one of his eponymous hotels if he bought the territory.

The US President tweeted a meme depicting the golden Trump International Hotel Las Vegas towering over modest, primary-coloured houses along a rocky coast.

I promise not to do this to Greenland! pic.twitter.com/03DdyVU6HA — Donald J. Trump (@realDonaldTrump) August 20, 2019

The meme first appeared on Twitter on Thursday with the caption: "Greenland in 10 years."

Denmark colonised the 772,000 square-mile island in the 18th century. It is home to only about 57,000 people, most of whom belong to the indigenous Inuit community.

It wouldn’t be the first time an American leader tried to buy Greenland.

In 1946, the US proposed to pay Denmark $100 million to buy Greenland after flirting with the idea of swapping land in Alaska for strategic parts of the Arctic territory.

The US already has a major airbase in the north-west of the island, housing 600 personnel. Thule Air Base in Greenland is the US military's northernmost installation.