US President Donald Trump has made light of his suggestion to buy Greenland by posting a doctored picture of Trump Tower looming over a small village there.

"I promise not to do this to Greenland!" he joked.

Donald Trump's tweet making light of buying Greenland

It comes after he said on Sunday he was "strategically" interested in a deal to buy the Arctic territory.

However, Denmark's prime minister was quick to remark and said Greenland was not for sale and the idea of selling it to the US is absurd.

“Greenland is not for sale. Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously,” Danish Prime Minister Mette Frederiksen told the newspaper Sermitsiaq during a visit to Greenland on Sunday.

Trump is due to visit Copenhagen early next month, when the Arctic will be on the agenda in meetings with Frederiksen and Prime Minister Kim Kielsen of Greenland, an autonomous Danish territory.

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