Greenland would choose to remain Danish over a US takeover, its leader said on Tuesday, ahead of White House talks on the future of the Arctic island which US President Donald Trump has repeatedly threatened.

Trump has been talking up the idea of buying or annexing the autonomous territory for years, and further stoked tensions this week by saying the United States would take it "one way or the other."

"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," Greenland's Prime Minister Jens-Frederik Nielsen said at a press conference.

"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."

He was speaking alongside Danish leader Mette 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.

Danish Foreign Minister Lars Lokke Rasmussen and his Greenlandic counterpart Vivian Motzfeldt are to meet US Vice President JD Vance and US Secretary of State Marco Rubio on Wednesday to discuss Greenland's future.

Lokke said they had requested a meeting with Rubio, and Vance had asked to take part and host it at the White House.

Vance made an uninvited visit to the island in March where he criticised Denmark for what he said was a lack of commitment to Greenland and security in the Arctic, and called it a "bad ally."

The comments enraged Copenhagen, which has been an ardent trans-Atlantic supporter and which has sent troops to fight US wars in Iraq and Afghanistan. (AFP)