Denmark’s prime minister has had a phone conversation with US President Donald Trump, who earlier this week scrapped a visit to the country by saying Mette Frederiksen was “nasty” when she rejected his idea of buying Greenland as an absurdity.

The prime minister’s office said Friday that the two spoke late on Thursday, and Danish media reported that the call was “constructive”.

Ms Frederiksen’s office says details of the discussion will not be released.

President Donald Trump (Alex Brandon/AP)

It is believed that it was first time the two spoke since Ms Frederiksen, who repeatedly has said the US remains one of Denmark’s close allies, took office on June 27.

Mr Trump cancelled a September 2-3 trip to Denmark as part of a European tour.

She also had said that Denmark does not own Greenland, which belongs to its people.

The scarcely populated island is part of the Danish realm and has its own government and parliament.

The political brouhaha over the world’s largest island comes from its strategic location in the Arctic.

Global warming is making Greenland more accessible to potential oil and mineral resources.

Race For The Arctic
Student researchers sit on top of a rock overlooking the Helheim glacier in Greenland (Felipe Diana/AP)

Russia, China, the US, Canada and other countries are racing to stake as strong a claim as they can to Arctic lands, hoping they will yield future riches.

The sparsely populated island, which is four times zones behind Copenhagen, became a Danish colony in 1775 and remained that way until 1953, when Denmark revised its constitution and made the island a province.

In 1979, Greenland and its 56,000 residents, who are mainly indigenous Inuits, got extensive home rule but Denmark still handles its foreign and defence policies, as well as currency issues.

Denmark pays annual subsidies of 4.5 billion kroner (670 million US dollars) to Greenland whose economy otherwise depends on fisheries and related industries.