Donald Trump may have expressed an interest in acquiring Greenland for the US, but Denmark thinks the idea is frankly insane and Greenlanders have pointed out their home is not actually for sale.

According to the Wall Street Journal, the US president has asked his aides and the White House counsel to look into the possibility of buying the world’s largest island, a largely autonomous country of the kingdom of Denmark.

The Greenland government was diplomatic, saying it had a good working relationship with the US and saw the inquiry as “an expression of general greater interest in investing in our country and its opportunities”. But it added firmly: “Greenland is obviously not for sale.”

In comments echoed in somewhat stronger terms by other politicians in both Greenland and Denmark, Ane Lone Bagger, Greenland’s foreign minister, confirmed the country was “open for business, but not for sale”.

Greenland MFA 🇬🇱 (@GreenlandMFA) #Greenland is rich in valuable resources such as minerals, the purest water and ice, fish stocks, seafood, renewable energy and is a new frontier for adventure tourism. We're open for business, not for sale❄️🗻🐳🦐🇬🇱 learn more about Greenland on: https://t.co/WulOi3beIC

Aaja Chemnitz Larsen, an MP from the Inuit Ataqatigiit party, Greenland’s second largest, said the response was “a ‘no thanks’ from here”. The island was not “a commodity that could be sold”, she said, and it was “tremendously uncomfortable to hear it discussed in such terms”.

Larsen told the Berlingske newspaper it would be better all round for Greenland to stay with Denmark and eventually be granted full independence. “If we were bought by the US, our welfare system would be dismantled and fundamental changes would be made to Greenlandic society,” she said. “We’d be crushed.”

Facebook Twitter Pinterest Aaja Chemnitz Larsen: ‘It’s a a “no thanks” from here’.

There is a large majority of support for independence in Greenland, although little certainty about how the country would survive without funding from Denmark.

Larsen said a majority of Greenlanders “clearly think it is better to have a relationship to Denmark than the US in the long term.” Trump’s reported interest in the country was not flattering, she said, because it was “Greenland’s geostrategic location that he’s interested in. Not the country itself, or Greenlanders.”

Eighty per cent of Greenland’s 836,000 sq miles (2.16m sq km ) are covered in ice, and its 56,000 inhabitants are concentrated mainly around the coastlines and in the capital, Nuuk. The island has home rule from Denmark in most domestic matters but Copenhagen is in charge of defence and foreign affairs.

Profile Greenland Show Hide About 80% of the world's largest island is covered in ice. Inuit people first inhabited it by moving from present-day Canada 4,000-5,000 years ago. It was named by Erik the Red when he led a fleet of 25 ships from Iceland to colonise it in 985 AD. Population: 56,000 - 90% of whom live in 16 towns. Size: 836,000 sq miles (2.16m sq km) - roughly the same size as Great Britain, France, Germany, Spain, Italy, Austria, Switzerland and Belgium combined. Official language: Greenlandic - closely related to languages spoken by Inuit in Canada and Alaska.

National dish: Meat soup called suaasat which normally contains seal, whale, reindeer or seabirds.

Life expectancy: 72.9 years

Head of state: Queen Margrethe II of Denmark

Premier: Kim Kielsen

Capital city: Nuuk (population 18,000)

National anthem: Nunarput Utoqqarsuanngoravit, adopted in 1916. The first verse translates as: “Our country, which has become so old, your head is all covered with white hair. Always held us, your children, in your bosom, and gave us the riches of your coasts.”

Religion: Christianity was introduced to the island around 1000 by Erik the Red’s son Leif Eriksson.

Government: Denmark granted the island limited self-government in 1979, 26 years after it was incorporated into the country by the Danish constitution. Further powers were devolved in 2008. Economic self-sufficiency has been a stumbling block to the island gaining full independence.

EU membership: Greenland was a member of the European Union as part of Denmark from 1973 to 1985. It withdrew in 1985 after 53% of people voted to leave in a referendum called following disputes over fishing rights.

Military: There is no military force. Defence and foreign policy remain in the hands of the Danes.

Airports: 14. The first three were built in the 1940s and 50s by the US, which was handed the defence and control of Greenland while Denmark was under Nazi occupation.

Famous Greenlanders: Jesper Grønkjær, played football for Ajax, Chelsea, Atlético Madrid; Rasmus Lerdorf, co-authored the PHP programming language; Aleqa Hammond, the country’s first female prime minister. Photograph: EIL Austria / Nasa / Alamy/www.alamy.com

Greenland is also home to the Thule air base, the US military’s northernmost outpost, built in 1951. About 750 miles inside the Arctic Circle, the radar and listening station employs 600 personnel and is an important part of America’s global defence system.

Ordinary Greenlanders were outraged. “They tried to buy us in the past, back in the 19th century, and again after the second world war,” one resident, Bent Abeelsen, said. “Now they are trying again. But it’s not going to happen”.

Else Mathiesen told local media Trump’s plans betrayed “an age-old mindset ... You can’t just buy an island or a people. This sounds like something from the era of slavery and colonial power, when you could just take over a country.”

Facebook Twitter Pinterest The Ilulissat icefjord near Ilulissat, Greenland. Most of the country is covered in ice. Photograph: Sean Gallup/Getty Images

For Indalik Høegh, the president’s plan was “just inside his head”. The island’s economy was “really not so good – it’s not surprising many Greenlanders move to Denmark. But really, it’s impossible to see Greenland becoming American.”

Danish politicians, for their part, reacted with astonishment. “It must be an April Fools’ Day joke … but totally out of season,” tweeted the former prime minister Lars Løkke Rasmussen, who heads the centre-right opposition.

Søren Espersen, of the nationalist Danish People’s party, said that if the story was true, “it is definitive proof that [Trump] has gone crazy. I have to say it as it is: the idea that Denmark would sell 50,000 citizens to the US is completely insane.”

Martin Lidegaard, of the Social Liberal party, described Trump’s reported remarks as “hopefully a joke, but otherwise a terrible idea”, while Uffe Elbæk, the leader of the progressive Alternative party, said it made Trump’s upcoming official visit to Copenhagen “the most absurd in living memory”.

Trump plans to make his first formal visit to Denmark on 2 September, meeting the country’s new Socialist prime minister, Mette Frederiksen – who herself will make her first official visit to Greenland next week – and attending a state banquet with Queen Margrethe II.

Pernille Skipper, of the Red-Green Alliance, said it “says a lot about Trump that he actually thinks you can buy a whole country and a whole people. Greenland is the Greenlanders, and this is not the 19th century. Not for sale.”

Danes were not the only non-Greenlanders to express dismay. “Oh dear lord. As someone who loves Greenland, has been there nine times to every corner and loves the people, this is a complete and total catastrophe,” tweeted Rufus Gifford, a former US ambassador to Denmark.

Denmark has, though, sold territories in the past. With the blessing of their inhabitants, it ceded the then Danish West Indies – now the US Virgin Islands – to the US in 1917 for $25m. The US also weighed buying Greenland in 1946 for $100m, after flirting with the idea of swapping land in Alaska for strategic parts of the island.