President Donald Trump has said he believes the US will gain control of Greenland, after showing renewed interest in acquiring the autonomous Danish territory in recent weeks.

"I think we're going to have it," he told reporters on Air Force One on Saturday, adding that the island's 57,000 residents "want to be with us".

His comments come after reports that Danish Prime Minister Mette Frederiksen insisted Greenland was not for sale in a fiery phone call with the president last week.

Trump floated the prospect of buying the vast Arctic territory during his first term in 2019 and has said US control of Greenland is an "absolute necessity" for international security.

"I think the people want to be with us," Trump said when asked about the island in the press room on board the presidential plane.

"I don't really know what claim Denmark has to it, but it would be a very unfriendly act if they didn't allow that to happen because it's for the protection of the free world," he added.

"I think Greenland we'll get because it has to do with freedom of the world," Trump continued.

"It has nothing to do with the United States other than that we're the one that can provide the freedom. They can't."

Despite Trump's apparent confidence, the prime ministers of Greenland and Denmark have both previously said the island was not for sale.

Greenland's PM Mute Egede said use of the territory's land was "Greenland's business", though he did express a willingness to work more closely with the US on defence and mining.

Meanwhile, Danish premiere Frederiksen said earlier this month that "Greenland belongs to the Greenlanders", and only the local population could determine its future.

Frederiksen reasserted her position in a heated 45-minute phone exchange with Trump last week, according to a report in the Financial Times.

The newspaper quoted an anonymous European official as saying the conversation was "horrendous", and another saying Trump's interest in acquiring Greenland was is "serious, and potentially very dangerous".

The Danish prime minister reportedly insisted the island was not for sale, but noted the US's "big interest" in it.

Greenland lies on the shortest route from North America to Europe, making it strategically important for the US. It is also home to a large American space facility.

In recent years, there has been increased interest in Greenland's natural resources, including mining for rare earth minerals, uranium and iron.

Though the island has wide-ranging autonomy, it remains part of the kingdom of Demark.

But there is a general consensus in Greenland that it will eventually become independent, which could pave the way for a new kind of relationship with the US.

President Trump's claim that the people of Greenland "want to be with us" may come as a surprise to some of the island's residents.

A fishing boat captain in the Kapisillit settlement told the BBC Trump was "welcome to visit" the island, but that "Greenland belongs to Greenlanders".

And local church elder Kaaleeraq Ringsted said Trump's language was "not acceptable", adding "Greenland is not for sale".

There are several ways Trump could pursue his desire to take over the territory. Asked earlier in January whether he could rule out using military or economic force, Trump said he could not.

His recent comments have sent shockwaves through the Danish political establishment, sparking hastily organised high-level meetings in Copenhagen earlier this month.