"Greenland is not for sale. Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously," Danish Prime Minister Mette Frederiksen told the newspaper Sermitsiaq during a visit to Greenland.
Trump, however, said Sunday afternoon that the idea of buying Greenland from Denmark came up in conversations within his administration and that it's essentially "a large real estate deal."
In remarks to reporters Sunday, Trump cast the possible purchase as a strategic move by the U.S. but not a top priority for his administration.
Trump suggested that Greenland is an economic burden for Denmark, saying Denmark loses almost $700 million a year "carrying it." He also described Denmark as a very good ally and a country that the U.S. protects as it does other portions of the world.
Trump's is due to visit Copenhagen early next month, when the Arctic will be on the agenda in meetings with Frederiksen and Prime Minister Kim Kielsen of Greenland, an autonomous Danish territory.
White House economic adviser Larry Kudlow on Sunday confirmed media reports earlier in the week that Trump had privately discussed with his advisers the idea of buying Greenland.
"I don't want to predict an outcome, I'm just saying the president, who knows a thing or two about buying real estate, wants to take a look at a Greenland purchase," Kudlow told Fox News.
Kudlow said the situation was "developing" and noted that U.S. President Harry Truman also had wanted to buy Greenland.
"And Denmark owns Greenland, Denmark is an ally, Greenland is a strategic place, up there. And they've got a lot of valuable minerals," Kudlow added.
A defense treaty between Denmark and the United States dating back to 1951 gives the U.S. military rights over the Thule Air Base in northern Greenland.
Greenland, located between the North Atlantic and Arctic oceans, is dependent on Danish economic support. It handles its own domestic affairs while Copenhagen looks after defense and foreign policy.
"It's an absurd discussion, and Kim Kielsen has of course made it clear that Greenland is not for sale. That's where the conversation ends," Frederiksen told the Danish broadcaster DR.
On Friday, Greenland's foreign minister, Ane Lone Bagger, had told Reuters: "We are open for business, but we're not for sale."