President Trump questioned the legitimacy of Denmark’s claims to Greenland over the weekend while amping up rhetoric for his plans for the U.S. to acquire the Danish-held region.

On Wednesday, Trump said he reached the “framework of a future deal” on Greenland with NATO Secretary General Mark Rutte , in a social-media post from Davos . He didn’t elaborate on the details but suggested it will benefit U.S. national security and access to minerals. NATO said negotiations will continue between Greenland, Denmark and the U.S.

Greenland’s prime minister, Jens-Frederik Nielsen , had previously said his country didn’t want to be a U.S. territory. “Greenland does not want to be controlled by the U.S. Greenland does not want to be owned by the U.S.,” Nielsen said.

Here’s what to know about Denmark’s history with the vast, potentially mineral- and energy-rich territory .

Danish claim to Greenland dates back to Norse Vikings

Over the weekend Trump texted Norway’s prime minister, “There are no written documents, it’s only a boat landed there hundreds of years ago, but we had boats landing there, also.”

Trump is partly right. The Danish claim dates back to the first few times Europeans set out to find new lands across the Atlantic Ocean, and specifically to the saga of Erik the Red.

Norse Vikings had been aware of lands to the west of Iceland since the ninth century. They were intrepid sailors and had already put down roots in Iceland, the Faroe Islands and the northern reaches of Scotland.

But it wasn’t until Erik was exiled in around 985 for killing another man that the Norse made their first settlement among the fjords of southern Greenland, centuries before Christopher Columbus set out to find a faster route to Asia.

Denmark kept control of Greenland after splitting with Norway.

The Norse stayed there for decades if not centuries, making the region part of an ocean-spanning empire governed from Norway. There is evidence to suggest that Leif Erikson, Erik’s son, went on to explore the lands around what is now Newfoundland.

By the time Denmark and Norway became a single kingdom in the 16 undefined century, contact with Greenland had largely been lost. Norwegian priest and missionary Hans Egede set out to reconnect with Greenland and convert whoever was there to Protestantism and found an Inuit community. Centuries of slow colonization and conversion followed.

Later, when Denmark and Norway split apart in the 19th, Norway formed a union with Sweden, while, crucially, Denmark kept hold of Greenland.

Has the U.S. tried to purchase Greenland before?

Secretary of State William H. Seward had previously proposed buying Greenland and Iceland from Denmark after securing Alaska from Russia in 1867. Then in World War II the U.S. deployed a military presence on the island to deter any aggression from Nazi Germany, which was then occupying Denmark. At the war’s close, President Harry Truman made a secret offer to buy Greenland for $100 million in gold, which Denmark rejected.

In the decades that followed, the U.S. expanded its military presence on Greenland while, politically, the island came under closer Danish control.

But now opinion polls suggest a majority of Greenlanders would now like to see full independence one day.

At the same time, both Russia and China have been expanding their activities in the region in recent years, putting the U.S. on edge and potentially undermining Trump’s plans to dominate what is likely to become an increasingly important part of the world in the decades to come.

U.S. has records of Danish control of the territory.

While Trump says there are no written documents to support the Danes’ claim to the territory, U.S. State Department records suggest otherwise.

The U.S. actually affirmed Denmark’s sovereignty over Greenland in 1916 as part of a deal to buy islands in the Caribbean from Denmark.

“The Government of the United States of America will not object to the Danish Government extending their political and economic interests to the whole of Greenland,” according to the State records . The Senate approved the agreement in 1916 and President Woodrow Wilson ratified it the following year, according to the State record.

This explanatory article may be periodically updated.

Write to James Hookway at James.Hookway@wsj.com