NUUK, Greenland—Daniel Thorleifsen has a suggestion for President Trump: Maybe try playing golf here first before putting in a bid for Greenland.

The nine-hole course Mr. Thorleifsen oversees as president of Nuuk Golf Club is open only four months a year. The rest of the time it is covered in snow. Players scramble over crags and stomp on wild berries to navigate from tee to tee while Air Greenland turboprops roar onto the airstrip nearby.

“He’s welcome to play if he came here. But he would find it very hard,” Mr. Thorleifsen said.

Mr. Trump has become entranced by the idea of the U.S. buying this vast, ice-shrouded island on the roof of the world, people familiar with discussions said. President Trump on Sunday confirmed his interest in potentially purchasing Greenland, but said it wasn’t a priority. The territory’s appeal seems rooted in its natural resources in addition to providing the U.S. with another doorstep to the Arctic as the ice sheet shrinks.

But the president’s interest has drawn mixed reactions in Nuuk, the country’s capital, a sparse city just 150 miles south of the Arctic Circle. Lapped by the Labrador Sea, its low-rise, brightly painted houses and apartment blocks are home to around a third of Greenland’s 56,000 inhabitants.

For some, the idea of buying and selling their homeland is a highhanded reminder of a painful and unresolved colonial legacy, which saw its indigenous inhabitants’ culture and language suppressed during centuries of rule from faraway Copenhagen. Others discern in the president’s apparent fascination a sign of the geostrategic importance of the self-governing territory, which is part of the Kingdom of Denmark. Many simply see it as a joke.

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All insist that Greenland isn’t for sale, as do its political leaders.

All insist that Greenland isn’t for sale. “People I know say ‘no thanks,’ ” said Helene Elisasen.

“People I know say ‘no thanks,’ ” said Helene Elisasen, as she threaded fishing lines with bait in the harbor to catch halibut at sea.

Greenland is the world’s largest island, covering more than 800,000 square miles in the North Atlantic and Arctic Sea northeast of Canada. It is larger than Mexico and around the same size as Saudi Arabia. Around 80% of the country is cloaked in ice, with human settlements hugging the coast. A network of airstrips and helipads, some dating from World War II, allow residents to jump from city to city in the absence of major roads.

Its economy is sustained by shrimp and fish exports and a $591 million annual subsidy from Denmark. Growing industries include tourism and mining. Active mines churn out rubies and minerals used to make fiberglass, and projects are under way to assess the feasibility of mining rare earths and uranium, Greenlandic officials say.

The abundant resources mean any buyer for Greenland would struggle to make a fair offer for the country, said Pavia Zeeb, a fisherman. “It’s too expensive,” he said.

Many Greenlanders like to relax by hunting caribou in the wilderness. Workplaces in Nuuk empty during the summer whenever a whale catch lands so that every household can grab a share, locals say. The raw liver of a newly killed seal is a prized delicacy.

Traditional Inuit tattoo artist Maya Sialuk described the idea of the U.S. buying Greenland as insensitive and rude.

Maya Sialuk practices traditional Inuit tattooing, an ancient art her ancestors used to ward off illness and seek good fortune when hunting and fishing. She described the idea of the U.S. buying Greenland as insensitive and rude.

“We are still trying to recover from a colonization period of almost 300 years,” she said. “Then there is this white dude in the States who’s talking about purchasing us.”

Whether the president’s aspiration is serious or not, Washington will continue to view Greenland as vital to American national-security interests. A decades-old defense treaty between Denmark and the U.S. gives the U.S. military virtually unlimited rights in Greenland at America’s northernmost base, Thule Air Base, which houses part of a U.S. ballistic missile early-warning system.

Greenland’s strategic importance to the U.S. was underscored further last year when the Pentagon worked successfully to block China from financing three airports on the island. With American prodding, Denmark’s government instead asked a consortium led by

Danske Bank

to help assemble an alternative financing package.

The nine-hole course Mr. Thorleifsen oversees as president of Nuuk Golf Club is open only four months a year.

In Copenhagen, which still sets Greenland’s foreign and defense policies, news of Mr. Trump’s enthusiasm for the territory has been interpreted as the latest signal from Washington that the U.S. is an engaged player in the Arctic, a zone of increasing economic and strategic rivalry with both China and Russia.

“The U.S. wants to make everyone aware the U.S. is an Arctic power,” said Nils Wang, a retired Royal Danish Navy rear admiral and director of Naval Team Denmark, an association for navy suppliers.

Denmark, too, aims to explore new research and economic opportunities as the Arctic opens up, and has warned that Greenland will lose its annual subsidy if it pushes for independence. Mr. Trump is due to meet the Danish and Greenlandic premiers during a previously planned visit to Copenhagen next month, alongside the leader of the Faroe Islands, another autonomous Danish region.

Múte Bourup Egede, leader of the left-wing, pro-independence Inuit Ataqatigiit party in Greenland’s parliament.

Múte Bourup Egede, leader of the left-wing, pro-independence Inuit Ataqatigiit party in Greenland’s parliament, said such strategic games—and Mr. Trump’s icebound fantasy—serve to remind Greenlanders of their country’s outsize importance in world affairs.

“America will always have an interest in Greenland,” said Mr. Egede, cradling a Bernie Sanders 2016 coffee mug. “Our country will always be ours.”

Write to Jason Douglas at

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