"We are now facing a geopolitical crisis, and if we have to choose between the United States and Denmark here and now, we choose Denmark," Greenlandic Prime Minister Jens-Frederik Nielsen said at a joint press conference with Danish counterpart Mette Frederiksen in Copenhagen.
Trump has further stoked tensions by saying on Sunday that the United States would take the territory "one way or the other".
"One thing must be clear to everyone: Greenland does not want to be owned by the United States. Greenland does not want to be governed by the United States. Greenland does not want to be part of the United States," Nielsen said.
He was speaking alongside Frederiksen, who said it had not been easy to stand up to what she slammed as "completely unacceptable pressure from our closest ally".
"However, there are many indications that the most challenging part is ahead of us," Frederiksen said.
Trump has insisted the US needs Greenland for "national security".
Frederiksen stressed that "of course, we want to strengthen cooperation on security in the Arctic with the United States, with NATO, with Europe and with the Arctic states in NATO."
Danish Foreign Minister Lars Løkke Rasmussen and his Greenlandic counterpart Vivian Motzfeldt are due to meet with US Vice President JD Vance and Secretary of State Marco Rubio at the White House on Wednesday.
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