Denmark is sending a clear "hands-off Greenland" message to United States President Donald Trump this week, through a three-day visit to the island by Prime Minister Mette Frederiksen.

Frederiksen said she wanted her visit to the massive, semi-autonomous Arctic island, which has been part of the Kingdom of Denmark for hundreds of years, to be seen as a show of support for its government, after months of comments from the US about Washington subjugating it.

"It has my deepest respect, how the Greenlandic people and the Greenlandic politicians handle the great pressure that is on Greenland," she said.

Frederiksen plans to hold talks with Greenland's incoming government during her stay, which is set to end on Friday.

Her visit follows one by US Vice-President JD Vance, who turned up at a US military base on Greenland on Friday, despite having been told by both Denmark and Greenland he was not welcome.

During his visit, Vance accused Denmark of underinvesting in the territory that Trump told Congress on March 4 he wants to control by "one way or another".

Frederiksen's visit comes as Greenland's incoming prime minister, Jens-Frederik Nielsen, is working to form a coalition government after having won the island's general election on March 11. He has so-far excluded participation in the coalition of the island's only pro-US political party.

Nielsen said earlier this week Frederiksen is welcome on the island and that, despite strong separatist sentiment there, Denmark will forever remain "Greenland's closest partner".

Nielsen, like almost all politicians on the island of 57,000 people, favors Greenland ultimately breaking away from Denmark but has said he is in no hurry to do so, especially with the US apparently waiting to swoop and take control of Greenland and its raw materials and increasingly navigable national waters.

The Reuters news agency said ahead of Frederiksen's visit that Nielsen is now hoping to strengthen ties with Denmark, until Greenland is ready to become a sovereign nation.

Nielsen has also said Greenland wants to establish a respectful relationship with the United States, Reuters added.

"Talking about annexation and talking about acquiring Greenland and not respecting the sovereignty is not respectful," Nielsen added. "So, let's start by being respectful to each other and build up a great partnership on everything."

After Trump repeatedly said he wants the US to control Greenland, and after he refused to rule out using military force to do so, Greenland and Denmark have become closer, Peter Viggo Jakobsen, an associate professor at the Danish Defense Academy, told the AP news agency.

"Trump has scared most Greenlanders away from this idea about a close relationship with the United States because they don't trust him," Jakobsen said.

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