Trump was due to arrive at the World Economic Forum on Wednesday, but a minor electrical issue on Air Force One has forced his plane to turn around.
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During a news conference at the White House, Trump was asked how far he was willing to go to acquire Greenland and replied, "You'll find out".
Meanwhile, French president Emmanuel Macron warned at a meeting at the World Economic Forum meeting in Davos, Switzerland of a "shift towards a world without rules", while Canadian Prime Minister Mark Carney said the "old order is not coming back".
Trump was due to arrive in Davos on Wednesday, but a minor electrical issue on Air Force One forced the plane to turn around.
It was unclear how the delay would impact his schedule. The White House said the plane turned around and that Trump would fly to Davos on another aircraft.
Trump has said there are "a lot of meetings scheduled on Greenland".
Earlier, during the lengthy press briefing, Trump also told reporters that "things are going to work out pretty well" in Greenland.
Asked by the BBC whether the possible break up of the Nato alliance was a price the president was willing to pay for Greenland, he responded, "Nobody has done more for Nato than I have, in every way," and said "Nato is going to be happy and we are going to be happy," adding, "We need it for world security."
But he earlier questioned whether Nato would come to aid of the US, should it be required.
"I know we'll come to (Nato's) rescue, but I just really do question whether or not they'll come to ours," he told reporters.
Nato - the North Atlantic Treaty Organization - currently has 32 member states, with the US one of the 12 founding countries.
Designed to safeguard freedom and security through a collective defence, one of the core principles of the Nato alliance is outlined in Article 5, which says that an armed attack against one or more mem