Since coming to power in January, Trump has repeatedly insisted that he wants the self-governed territory to be in Washington's grip, refusing to rule out the use of force to do so.
"We need Greenland for international safety and security. We need it. We have to have it," Trump told podcaster Vince Coglianese on Wednesday. "I hate to put it that way, but we're going to have to have it."
"I think we'll go as far as we have to go," he then told journalists later the same day, as reported by news agency Reuters.
He also said Denmark would be forced to give in to his demands over the territory, stating "Denmark has to have us have Greenland."
Asked during the podcast if he thought Greenlanders were eager to join the United States, Trump said he did not know. Polls have shown a large majority of Greenlanders do not want this.
"We have to convince them," Trump said. "And we have to have that land, because it's not possible to properly defend a large section of this Earth, not just the United States, without it."
Trump's comments prompted Danish Prime Minister Mette Frederiksen to say on her Facebook account: "We mustn't have illusions -- President Trump's interest in Greenland is not going away".
"They know that Greenland is not for sale. They know that Greenland doesn't want to be part of the United States," she added, saying the message had been communicated "unambiguously, both directly and in public."
Dogsled visit dropped
Trump's latest strident comments come as Vice President Vance is due to accompany his wife Usha on a visit to the US-run Pituffik Space Base in Greenland on Friday.
Frederiksen and Greenland's outgoing Prime Minister Mute Egede had earlier harshly criticised plans by a US delegation to visit the Arctic island uninvited for what was initially a much broader visit.
Egede had characterised the initial plans as "foreign interference," noting that the outgoing government had not "sent out any invitations for visits, private or official."
On Wednesday, Danish Foreign Minister Lars Løkke Rasmussen welcomed the decision to limit the visit to the US space base.
"I think it's very positive that the Americans have canceled their visit among Greenlandic society. They will only visit their own base, Pituffik, and we have nothing against that," he told public broadcaster DR.
Formerly known as Thule Air Base, the Pituffik Space Base is the United States' northernmost military installation and supports missile warning, missile defense and space surveillance missions.
The White House on Tuesday said the Vances' visit to the space base would take place in lieu of the second lady's scheduled visit to a dogsled race in Sisimiut, where an anti-US demonstration was reportedly planned.
READ ALSO: Is US change of plans over Greenland visit a deescalation?
Greenlandic officials have repeatedly said the territory does not want to be either Danish or American, but is "open for business" with everyone.
"There is no doubt we find ourselves in a tough situation," Frederiksen said of Trump's repeated comments on a takeover, predicting "a situation that will ebb and flow, maybe for a long time yet."
Following March 11th elections, Greenland has only a transitional government, with parties still in negotiations to form a new coalition government.
Marc Jacobsen, a senior lecturer at the Royal Danish Defense College, called the decision to limit the US visit "a deescalation," a term also used by Løkke.
"You do not come to another country when you haven't been welcomed," he told AFP.
Jacobsen added that the planned anti-US demonstration in Sisimiut, after a similar protest in the capital Nuuk on March 15th, may have also factored into Vance's decision to contain the visit.
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