Greenland does not need medical assistance from other countries, Denmark has said, after Donald Trump said he was sending a hospital ship to the autonomous Danish territory that he wants to acquire.

“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. So it’s not as if there’s a need for a special healthcare initiative in Greenland,” the country’s defence minister, Troels Lund Poulsen, told the Danish broadcaster DR on Sunday.

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

Mette Frederiksen, the Danish prime minister, defended Denmark’s healthcare system, writing on Facebook that she was “happy to live in a country where there is free and equal access to health for all. Where it’s not insurances and wealth that determine whether you get proper treatment.”

“You have the same approach in Greenland,” she said, before adding: “Happy Sunday to you all” in front of a blushing, smiling emoji.