The White House has praised Denmark as a US ally, as American officials scramble to repair the damage from Donald Trump's cancellation of his state visit to the Scandinavian nation.

Mike Pompeo, the secretary of state, told his Danish counterpart that Washington appreciated the country’s “cooperation as one of the United States’ allies and Denmark’s contributions to address shared global security priorities”, according to a State Department spokesman.

Danish foreign minister Jeppe Kofod said in a tweet that the pair had had a “frank, friendly and constructive talk” following Mr Trump’s outburst over the possibility of buying Greenland, which his government had rebuffed.

Their comments came as Carla Sands, the US ambassador to Denmark, insisted her boss “values & respects” the country and “looks forward to a visit in the future to discuss the many important issues in our strong bilateral relationship”.

She added on Twitter: “Great friends & Allies ... should be able to discuss all issues openly & candidly.”

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Mr Trump had been invited to Denmark by Queen Margrethe II.

But in an early-morning tweet on Wednesday the Republican said he would not travel to Copenhagen in September as planned because Mette Fredericksen, the Danish prime minister, had declined to discuss selling Greenland to the US.

The snub was all the more extraordinary because only a day earlier he had said the idea of purchasing the semi-autonomous territory – where the US already has a military presence – was “not number one on the burner”.

Mr Trump’s tweets also undercut Ms Sands, who had enthusiastically anticipated his visit in a separate Twitter post.

The president called Ms Fredericksen’s reaction to his apparent desire to buy Greenland “nasty” after the Danish premier said the idea was “absurd”.

“She’s talking to the United States of America. You don’t talk to the United States that way, at least under me,” he told reporters on Wednesday.

He added: “Greenland was just an idea, just a thought. But I think when they say it was ‘absurd’ and it was said in a very nasty, very sarcastic way, I said, ‘We’ll make it some other time’.”