Donald Trump says he has agreed to a "framework of a future deal" on Greenland after talks with NATO chief Mark Rutte in Switzerland.
The US president also said he would not go ahead with threatened new tariffs on European nations that were sending troops to the Danish territory.
Mr Trump made the announcement on social media after giving a speech in which he ruled out using military force to acquire Greenland.
"Based upon a very productive meeting that I have had with the Secretary General of NATO, Mark Rutte, we have formed the framework of a future deal with respect to Greenland and, in fact, the entire Arctic Region," Mr Trump wrote on Truth Social.
"This solution, if consummated, will be a great one for the United States of America and all NATO Nations.
"Based upon this understanding, I will not be imposing the Tariffs that were scheduled to go into effect on February 1st."
Mr Rutte, NATO's secretary-general, confirmed Mr Trump's announcement shortly after it was posted.
"His Truth Social post is exactly to the point, and I totally agree with that," Mr Rutte said.
Danish Foreign Minister said the deal would not lead to US ownership of Greenland. "That's a red line," he told Danish broadcaster DR.
A NATO spokesperson said future talks would "focus on ensuring Arctic security through the collective effort of Allies".
"Negotiations between Denmark, Greenland, and the United States will go forward aimed at ensuring that Russia and China never gain a foothold — economically or militarily — in Greenland."
Mr Trump's takeover threats and escalating rhetoric had overshadowed other issues at the World Economic Forum's annual meeting, and prompted European leaders to schedule a separate emergency summit in Brussels later in the week.
The leaders of Greenland and Denmark have been steadfastly opposed to ceding any sovereignty to the US, which already has military access, a base and troops on the island.
In a later interview with business channel CNBC, Mr Trump declined to give many additional details. "It's a little complex, but we'll explain later down the line," he said.
Asked if the deal involved ownership, critical mineral rights or his promised "Golden Dome" missile defence system, Mr Trump said: "They're going to be involved in the Golden Dome, and they're going to be involved in mineral rights, and so are we."
US markets rallied after the announcement. The Dow, S&P 500 and NASDAQ indices all finished the trading day up about 1.2 per cent.
'A small ask'
In his earlier speech, delivered to a packed room of world and business leaders in the Swiss city of Davos, Mr Trump said he wanted "immediate" negotiations on the issue.
However, he said "I won't use force" to capture Greenland, something he and members of his administration had previously hinted could happen.
At one point during his speech, delivered Wednesday, local time, Mr Trump appeared to speak directly to European leaders opposing a US takeover.
"You can say yes, and we will be very appreciative, or you can say no, and we will remember," he said.
Mr Trump, using some of his strongest rhetoric on the issue yet, described Denmark as "ungrateful".
Despite that, he also appeared to trivialise the demand at points, too, saying getting Greenland was "a small ask" for a "piece of ice".
"I'm seeking immediate negotiations to once again discuss the acquisition of Greenland by the United States," he said, after initially telling the room he had planned not to speak about the issue during his Davos address.
"I was going to leave it out of the speech," he said.
Mr Trump said he wanted control over Greenland, home to about 56,000 people, not because its natural resources could be valuable, but because of its strategic importance.
"We want a piece of ice for world protection, and they won't give it," the US president said.
Speaking after Mr Trump's address, Denmark's Foreign Minister Lars Lokke Rasmussen welcomed the US president's comments that the US would not use force to take Greenland and, once again, ruled out negotiating any sale.
Trade war threat
In the days leading up to his speech, the US president had threatened to impose additional tariffs on eight NATO countries that had pushed back on his position on Greenland.
In response, European lawmakers refused to ratify a trade agreement struck between the EU and US six months ago.
Mr Trump has singled out Norway this week, incorrectly claiming that it is refusing to award him the Nobel Peace Prize, for particular criticism.
But he has also railed against a UK government plan to return the Chagos Islands to Mauritius, and France, which declined an offer to join his global Board of Peace.
British Prime Minister Keir Starmer told parliament that Mr Trump's criticisms were an attempt to pressure him into backing Mr Trump's demand to own Greenland.
"He wants me to yield on my position, and I'm not going to do so," Sir Keir said, before Mr Trump took to the stage at Davos.
At multiple points during his speech, Mr Trump said he "loved" NATO and Europe, but that he was not convinced they would support the US.
His claims were at odds with the historical record. Multiple NATO allies, including Denmark, contributed troops and other resources to the US invasion of Afghanistan in the wake of the September 11 terror attacks.
Mr Trump spent much of his speech deriding his predecessor, Joe Biden, and talking up his country's economic figures.
"People are doing very well, they're very happy with me," he said, despite multiple polls showing the US president's approval rating plummeting.
He spoke for more than an hour and, on several occasions, appeared to confuse Greenland with Iceland.
"Our stock market took the first dip yesterday because of Iceland," he said at one point. "So Iceland's already cost us a lot of money."
