Greenland's prime minister has asked US President Donald Trump to speak with him rather than making "random outbursts on social media", after Trump said he was sending a US hospital ship to "take care" of people on the island.

Trump wrote on Truth Social that he was going to send a boat filled with medical supplies, alleging "many people" on the island are sick and "not being taken care of".

Jens-Frederik Nielsen responded, "It's going to be a no thanks from us," and said that Greenland provides free healthcare for all citizens, unlike the US.

Trump has long coveted the vast Arctic island - but conceded in January that he would not take it by force, after previously refusing to rule it out.

He later announced a "framework for a future deal" around the US and Greenland, after Denmark and Nato allies made it clear that they would not give in to his calls to relinquish sovereignty.

In his post on social media, Trump said that he and his Greenland envoy Jeff Landry were "going to send a great hospital boat to Greenland to take care of the many people who are sick, and not being taken care of there. It's on the way!!!"

The post included what appeared to be an illustrated or AI image of the USNS Mercy, one of two hospital ships operated by the US navy. It is not clear if Trump was referencing either of those ships, or what had prompted his decision.

Responding to the post, Nielsen said that Trump's idea "is noted. But we have a public healthcare system where treatment is free for citizens."

"It's not like that in the United States, where it costs money to go to the doctor," he wrote on Facebook.

Nielsen added that Greenland remained open to cooperating with the US but underlined the importance of discussing issues directly.

"Talk to us instead of just making more or less random outbursts on social media," he said.

Trump's post came soon after Denmark's Joint Arctic Command said it had evacuated a crew member who required urgent medical treatment from a US submarine close to Nuuk. It is not clear if Trump's post was related to the incident.

A month on from Trump announcing a "framework for a future deal" over Greenland, details are still unclear, though earlier this month US vice president JD Vance alleged that European countries were "willing to make a lot of accommodations".