Washington DC - President Donald Trump refused Tuesday to say how far he will go on Greenland but suggested that he could make a deal as European leaders voice alarm over his threats to seize the territory from ally Denmark.

Asked hours before he was to head to the World Economic Forum in Davos, Switzerland how far he would go, Trump replied only: "You'll find out."

"We have a lot of meetings scheduled on Greenland, and I think things are going to work out pretty well," Trump told reporters about his Davos meetings.

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Denmark has warned that the entire NATO alliance is at risk if Trump moves forward on threats. Over the weekend, Trump vowed fresh tariffs on European countries, including Britain, France, and Germany, which sent troops to Greenland in solidarity.

He dismissed suggestions that he was putting at risk a deal last year with the EU in which the allies promised to ramp up investment in the US, saying "They need that agreement very badly with us."

"I think that we will work something out where NATO is going to be very happy and where we're going to be very happy," Trump said.

"But we need it for security purposes. We need it for national security and even world security," Trump said of Greenland.

Greenland's leadership has repeatedly said that the vast but sparsely populated island is not for sale.

Asked about the broad opposition to his designs among Greenland's population, Trump said, "When I speak to them, I'm sure they'll be thrilled."

Trump has claimed that the US needs Greenland, which would dramatically increase the US land mass, because of a threat of Russia or China seizing the island as climate change opens up Arctic water routes.

Neither of the two rival powers claims Greenland, and Denmark has said that China has no major investment and has not recently sent any warship to Greenland.