Copenhagen, Denmark - Denmark and its territory, Greenland, on Sunday rejected Donald Trump's offer to send a naval hospital ship to the Arctic island coveted by the US leader.

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.

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"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 specialized treatment, they receive it in Denmark."

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