US President Donald Trump has cancelled a state visit to Denmark after the nation's prime minister said Greenland was not for sale to the US.

The president was scheduled to visit on 2 September, at the invitation of Denmark's Queen Margrethe II.

Then last week Mr Trump suggested the US was interested in buying Greenland, an autonomous Danish territory.

Danish PM Mette Frederiksen described the suggestion as "absurd" and said she hoped Mr Trump was not being serious.

Ms Frederiksen is due to give a statement later on Wednesday.

How did we get here?

While praising Denmark as a "very special country", Mr Trump said in a tweet on Tuesday that his planned visit would no longer go ahead because Ms Frederiksen had "no interest in discussing the purchase of Greenland".

The cancellation was confirmed by a White House spokesman.

The Danish royal house also confirmed it had been informed of the cancellation. The house's head of communications, Lene Balleby, told the BBC "it was definitely a surprise".

Just hours before Mr Trump announced the cancellation, the US ambassador to Denmark, Carla Sands, tweeted: "Denmark is ready for the POTUS @realDonaldTrump visit! Partner, ally, friend."

Mr Trump had earlier confirmed reports that he was interested in buying Greenland. When asked on Sunday if he would consider trading a US territory for the island, he replied: "Well, a lot of things could be done."

"Essentially it's a large real estate deal," he said. Then, on Monday, the US president posted an image on social media showing a tall golden skyscraper among the homes of a small village on the island.

How have Greenland and Denmark reacted?

Mr Trump's suggested purchase was dismissed by Greenlandic and Danish officials. "Greenland is not for sale, but Greenland is open for trade and co-operation with other countries, including the USA," said the territory's premier, Kim Kielsen.

Lars Lokke Rasmussen, the former Danish prime minister, tweeted: "It must be an April Fool's Day joke."

Soren Espersen, foreign affairs spokesman for the populist Danish People's Party, told national broadcaster DR: "If he is truly contemplating this, then this is final proof that he has gone mad."

Danish Conservative MP Rasmus Jarlov, who earlier said that "of all things that are not going to happen, this is the most unlikely", accused Mr Trump of lacking respect for his country in a tweet on Wednesday.

Why would Greenland appeal to Trump?

Mr Trump has reportedly taken an interest in Greenland, in part, because of its natural resources, such as coal, zinc, copper and iron ore.

But while Greenland might be rich in minerals, it currently relies on Denmark for two thirds of its budget revenue. It has high rates of suicide, alcoholism and unemployment.

President Trump confirmed reports he was interested in buying Greenland

Two people briefed on the discussions told the New York Times the president was also interested in Greenland's "national security value" because of its location.

The US has long seen the island, which sits along a direct route from Europe to North America, as being strategically important. It established the Thule air force and radar base there at the start of the Cold War, which now covers space surveillance and forms the northernmost part of the US ballistic missile early warning system.

Meanwhile, new Arctic sea routes are opening up as climate change continues to accelerate the melting of ice in the region.

Mr Trump's latest bid also comes at a time that China is taking a big interest in the area. Last year, a Chinese state-owned construction company announced plans to build new airports in Greenland - but withdrew them in June this year.

Republican Representative Mike Gallagher described Mr Trump's idea as a "smart geopolitical move".

"The United States has a compelling strategic interest in Greenland, and this should absolutely be on the table," he tweeted.

Where exactly is Greenland?

Greenland is the largest island in the world (after Australia, which is defined as a continent in its own right). It is an autonomous Danish territory, located between the North Atlantic and Arctic oceans.

It has a population of about 56,000 people concentrated around the coastline. Almost 90% are indigenous Greenlandic Inuit people. It has a limited self-government and its own parliament.

More than 80% of the island is covered by an ice cap which is feared to be melting due to global warming. The ice melt has increased access to the island's mineral resources.

But it is also believed that the receding ice may expose toxic nuclear waste that was left at several US military sites during the Cold War.

Has the US ever tried to buy the island before?

The idea of purchasing Greenland was first mooted during the 1860s under the presidency of Andrew Johnson.

In 1867, a report by the US State Department suggested that Greenland's strategic location, along with its abundance of resources, made it an ideal acquisition.

But no official move was made until 1946, when Harry Truman offered Denmark $100m for the territory. He had earlier toyed with the idea of swapping land in Alaska for strategic parts of Greenland, AP reported.