In his first extended comments since being appointed to the role this week, Louisiana Governor Jeff Landry on Tuesday said the Trump administration isn't going to "go in there trying to conquer anybody" or try to "to take over anybody's country."
The governor's comments seemed somewhat at odds with Trump, who has repeatedly said the US needs to take over the Arctic territory for the sake of US security and has not ruled out military force to take control of the mineral-rich, strategically located Arctic island.
"Well, I think our discussions should be with the actual people in Greenland — the Greenlanders," Landry said in an appearance on Fox News' The Will Cain Show.
"What are they looking for? What opportunities have they not gotten? Why haven't they gotten the protection that they actually deserve?"
Trump's announcement of Landry's appointment has once again stirred anxiety in Denmark and Europe.
Denmark's foreign minister told Danish broadcasters that he would summon the US ambassador to his ministry.
"We have said it before. Now, we say it again. National borders and the sovereignty of states are rooted in international law," Danish Prime Minister Mette Frederiksen and her Greenlandic counterpart, Jens-Frederik Nielsen, said in a joint statement on Monday.
"They are fundamental principles. You cannot annex another country. Not even with an argument about international security."
Trump called repeatedly for US jurisdiction over Greenland during his presidential transition and in the early months of his second term. In March, Vice President JD Vance visited a remote US military base in Greenland and accused Denmark of under-investing there.
The issue gradually drifted out of the headlines, but in August, Danish officials summoned the top US diplomat in Copenhagen following a report that at least three people with connections to Trump had carried out covert influence operations in Greenland.
The Trump administration did not offer any warning ahead of the announcement of Landry's appointment, according to a Danish government official, who spoke on condition of anonymity to discuss internal deliberations.
The administration also has yet to provide any details about the appointment to Congress, according to a congressional aide who was not authorised to comment publicly and spoke on the condition of anonymity.
Trump is renewing the Greenland debate at a moment when he has no shortage of foreign policy crises to dealing with, including maintaining a fragile truce in Gaza and negotiating an end to Russian President Vladimir Putin's brutal war in Ukraine.
