"If you look at the NATO treaty, the UN charter or international law, Greenland is not open to annexation," Løkke told reporters.
"I feel that Trump talks about this issue in many different ways, depending on who is asking. Yesterday, a journalist asked about annexation," he also said.
"Then we get reactions like this, which, at the core, probably reveal an American intention that we cannot fulfil," the Danish foreign minister said.
Asked by reporters in the White House Thursday about taking over the island, Trump said: "I think it will happen."
NATO Secretary General Mark Rutte who was meeting him at the time refused to be drawn.
"I don't want to drag NATO into that," he said.
The diplomatic general secretary then backed up Trump's point about Russian and Chinese interest in the Arctic region.
Despite Rutte's apparently noncommittal stance, Løkke said he is not in doubt about NATO’s support for Denmark.
"I'm absolutely certain that NATO will, of course, stand by Denmark. You cannot annex an allied country, or any other country, for that matter," he said.
"That would be a violation of international law, this is clearly stated," he said.
Greenland's outgoing Prime Minister Mute Egede meanwhile said "enough is enough" in relation to Trump's repeated promises to seize the territory. He said he was calling a meeting of party leaders to jointly reject Trump's remark.
"This time we need to toughen our rejection of Trump. People cannot continue to disrespect us," Egede wrote on Facebook.
READ ALSO: Greenlandic PM says Trump 'has not shown respect'
Egede continues to lead Greenland while awaiting the formation of a new government after his party's defeat in elections on Tuesday.
"The American president has once again evoked the idea of annexing us. I absolutely cannot accept that," he wrote.
"I respect the result of the election, but I consider that I have an obligation as interim head of government: I have therefore asked the administration to summon the party heads as soon as possible."
Jens-Frederik Nielsen, leader of the election winning centre-right Democrats and likely future Greenlandic prime minister, also criticised Trump's statement.
"Trump's statement from the US is inappropriate and just shows once again that we must stand together in such situations," Nielsen said in a post to Facebook.
READ ALSO: What are Greenlanders saying about Trump's takeover bid?
In his first stint as US president, Trump had evoked the idea of buying Greenland from Denmark -- an idea rejected by both Copenhagen and Greenlanders.
Since returning to power this year, Trump has stepped up his quest to acquire the territory, but in much more bellicose terms.
Trump claims the US needs to own Greenland for its own security.
According to polls, most Greenlanders support independence from Denmark but not annexation by Washington.
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