On Monday night, Trump tweeted an edited photo of a coastal town dotted with colorful homes – all dwarfed by a golden skyscraper bearing the US president’s name.

“I promise not to do this to Greenland!” Trump said.

The tweet came a day after he confirmed news reports that he was mulling the idea of buying the autonomous Danish territory, though he has acknowledged that such a deal is “not No 1 on the burner”.

Front of mind, perhaps, are warnings from economists that the US economy is teetering toward a recession. But Trump, ever the businessman, apparently cannot resist the prospect of what he has called “essentially a large real estate deal” with miles of coastline.

“Strategically it’s interesting and we’d be interested but we’ll talk to them a little bit,” Trump told reporters on Sunday.

News of the president’s interest in buying the icy island were met internationally with roars of laughter. But on the island and in Denmark, the response ranged from incredulous to indignant.

“I think he’s crazy,” one resident told CBS. Another said the idea felt “patronizing”.

The Danish prime minister has called any discussion of a sale “absurd”.

“Greenland is not for sale,” said Mette Frederiksen, the Danish prime minister. “Greenland is not Danish. Greenland belongs to Greenland. I strongly hope that this is not meant seriously.”

“We are open for business, but we’re not for sale,” Greenland’s foreign minister, Ane Lone Bagger, said.

Trump is scheduled to visit Denmark in September, as part of a trip to Europe.

Earlier on Monday, Trump’s son Eric shared the same photo of a Trump Tower in Greenland on Instagram.

He wrote: “I don’t know about you guys but I love the concept of buying Greenland.”

More about: #DonaldTrump   #Greenland