Greenland wants to work more closely with the US on defence and exploring its mining resources, its prime minister said on Monday.

Mute Egede said his government was looking for ways to work with President-elect Donald Trump, who has in recent weeks shown renewed interest in taking control of the territory – without ruling out using military or economic force to do so.

Also on Monday, Denmark's foreign minister said it was ready to work with Greenland to "continue talks" with Trump "to ensure legitimate American interests" in the Arctic.

Greenland, a largely autonomous Danish territory, 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 and has some of the largest deposits of rare earth minerals, which are crucial in the manufacture of batteries and high-tech devices.

Trump tried to buy Greenland during his first term in 2019 and has placed the issue back on his agenda as his second term approaches - calling it an "absolute necessity" for both American and international security.

Prime Minister Egede previously said Greenland was not and would not be "for sale," while emphasising the importance of staying open to "cooperation and trade with the whole world".

On Monday, he told a press conference in Copenhagen that his government was ready to start a dialogue with the incoming Trump administration.

But he added that the use of the territory's land was "Greenland's business".

"It is... Greenland that will decide what agreement we should come to."

Meanwhile, Denmark's foreign minister also addressed Trump's renewed interest in Greenland during a press conference in Jerusalem.

"I don't want to get into any dispute with the incoming president Trump," Lars Lokke Rasmussen said.

"He has a certain specific way to formulate requests, and what we are doing right now is getting into a more detailed dialogue with the incoming president."

"We agree that the Americans have certain concerns about the security situation in the Arctic, which we share," he said.

Rasmussen said Denmark, in close cooperation with Greenland, was ready to continue talks with Trump to ensure "legitimate American interests".

Trump has also expressed his desire to acquire the Panama Canal, and vowed to use "economic force" to absorb Canada into the US.