A day earlier, Trump said he was sending "a great hospital boat to Greenland to take care of the many people who are sick, and not being taken care of there".

But Greenlandic Prime Minister Jens-Frederik Nielsen, who heads the autonomous territory's government, wrote on his Facebook page: "That will be 'no thanks' from us."

"President Trump's idea to send a US hospital ship here to Greenland has been duly noted. But we have a public health system where care is free for citizens," he said.

"This is not the case in the United States, where going to the doctor costs money."

Danish Defence Minister Troels Lund Poulsen likewise told Danish broadcaster DR: "The Greenlandic population receives the healthcare it needs. They receive it either in Greenland, or, if they require specialised treatment, they receive it in Denmark."

He added: "It's not as if there's a need for a special healthcare initiative in Greenland."

On the day that Trump made his proposal, Danish forces evacuated a crew member of a US submarine off the coast of Greenland's capital Nuuk after the sailor requested urgent medical attention.

Denmark's Joint Arctic Command said in a post on Facebook that the crew member was flown to a hospital in Nuuk after an unspecified medical emergency on board the vessel.

- AI-generated hospital ship -

In Greenland, as in Denmark, access to healthcare is free for citizens. There are five regional hospitals across the vast Arctic island, with the one in the capital Nuuk serving patients from all over the territory.

Without explicitly mentioning the US proposal, Danish Prime Minister Mette Frederiksen said she was "happy to live in a country where access to healthcare is free and equal for all. Where insurance or wealth does not determine whether one receives dignified treatment".

Trump, in his Truth Social message on Saturday about the hospital ship, posted an AI-generated image of a US Navy medical vessel, USNS Mercy.

"It's on the way!!!" he added.

It was not immediately clear if that meant he was deploying that ship to Greenland.

The US president indicated the deployment was being carried out in coordination with Jeff Landry, appointed in December as the US Special Envoy to the Arctic island.

Aaja Chemnitz, who represents Greenland in the Danish Parliament, wrote on Facebook that, while Greenland's health system had its share of problems, they were best resolved through cooperation with Denmark.

Denmark, she noted, "is one of the wealthiest and most educated countries, for example in the field of healthcare," contrasting it with "the United States, which has its own healthcare system problems".

Earlier this month, Greenland signed an agreement with Copenhagen to improve the treatment of Greenlandic patients in Danish hospitals.

Denmark's central bank had warned in January that the Arctic island's public finances were under pressure from demographic trends, pointing to its ageing population and shrinking workforce.

- 'New normal' -

Trump has repeatedly said he believes the United States must control Greenland to ensure US national security.

Earlier threats he made to seize the territory, by force if necessary, have ebbed since he struck a "framework" deal with NATO Secretary General Mark Rutte to ensure greater US influence.

The defence minister, Lund Poulsen, told DR he was not aware of a possible arrival of the suggested US hospital ship.

"Trump is constantly tweeting about Greenland. So this is undoubtedly an expression of the new normal that has taken hold in international politics," he said.

Meanwhile, in Nuuk, where a third of the island's 57,000 inhabitants live, people are tired of the US president's repeated jabs.

"I don't care," a man said under sparse, icy snowfall when asked by AFP about Trump's recent remarks, while most people avoided journalists' questions.