US President Donald Trump said on Tuesday he had agreed to a meeting with "various parties" this week about Greenland as he stepped up pressure on European leaders at Davos over his demand to take the Arctic island from Nato ally Denmark.

Trump is expected to dominate the week-long gathering of global elites at the Swiss ski resort, putting the transatlantic alliance to the test with his push to take over the Danish autonomous territory.

Europe is weighing countermeasures after Trump threatened to impose tariffs on eight European countries over the Greenland standoff – though Washington has warned that any retaliatory levies will be "unwise".

Trump was not due to arrive at the World Economic Forum (WEF) until Wednesday, but was already overshadowing the agenda with a series of posts on his Truth Social platform, saying he had a "very good" call with Nato chief Mark Rutte over Greenland.

"I agreed to a meeting of the various parties in Davos, Switzerland," he said in the post late on Monday.

Trump said he did not think European leaders would "push back too much" on his attempt to buy the vast strategic island, telling reporters on Monday: "They can't protect it."

European Union chief Ursula von der Leyen and French President Emmanuel Macron will address the forum on Tuesday, along with Vice Premier He Lifeng and Canadian Prime Minister Mark Carney, whose countries have their own disputes with Trump.

Trump will deliver a speech on Wednesday and is scheduled to participate in other events on Thursday. A US delegation is already on the ground in Davos to promote an American agenda that has unsettled the global order cherished by the WEF.

While Macron will leave on Tuesday without seeing Trump in Davos, German Chancellor Friedrich Merz said he would seek to meet the US president at the forum on Wednesday.

Macron has instead sent a message to Trump to propose a G7 summit in Paris on Thursday on Greenland, as well as ways to end Russia's war with Ukraine, with Moscow and Kyiv attending on the sidelines.

But Trump's relations with Macron hit a new low on Monday when the US president threatened 200 percent tariffs on French wine over France's intention to decline an invitation to join his "Board of Peace".

Analysts have likened the board aimed at resolving international conflicts – which has a US$1 billion fee for a permanent spot – to a pay-to-play version of the UN Security Council.

Trump confirmed on Monday that Russian President Vladimir Putin was one of various world leaders invited to join, and said of Macron that "nobody wants him" as he will "be out of office very soon".

European Union leaders will hold an emergency summit in Brussels on Thursday to discuss their response to the Greenland crisis, one of the gravest in years to hit transatlantic ties. (AFP)