Denmark’s foreign minister has said there is a “fundamental disagreement” with the US over Greenland after talks at the White House.

Lars Lokke Rasmussen said the meeting with Vice-President JD Vance and Secretary of State Marco Rubio on Wednesday had been “frank but constructive”. But he added that US President Trump was insisting on “conquering” Greenland which was “totally unacceptable”.

“We made it very, very clear that this is not in the interest of [Denmark],” he said.

Trump afterwards reiterated his interest in acquiring the resource-rich island, a position that has rattled allies across Europe and stoked tensions with Nato.

The hour-long meeting between the US, Denmark and Greenland failed to bring a major breakthrough, although all sides agreed to set-up a high-level working group to discuss the future of the autonomous Danish territory.

Rasmussen said there were “red lines” the US could not cross, and the working group would meet in the coming weeks in an effort to find a compromise. He added that Denmark and Greenland were open to the possibility of the US opening more military bases on the island.

“It’s productive to start discussions at a high level,” he said.

Rasmussen also said there was an “element of truth” in Trump’s view that security should be bolstered to counter Russian and Chinese interests in the Arctic. But he said the president’s comments about the presence of Russian and Chinese warships around Greenland were “not true”.

Despite being a sparsely populated territory, Greenland’s location between North America and the Arctic makes it well placed for early warning systems in the event of missile attacks and for monitoring vessels in the region.

Trump has repeatedly said acquiring it is vital to US national security.

The US already has more than 100 military personnel permanently stationed at its Pituffik base in Greenland’s north-western tip, a facility that has been operated by the US since World War Two.

Under existing agreements with Denmark, the US has the power to bring as many troops as it wants to Greenland.

After the talks on Wednesday, Minister of Foreign Affairs of Greenland Vivian Motzfeldt said the territory was open to greater co-operation with the US but also opposed a takeover.

“We have shown where our limits are,” Motzfeldt said.

Vance and Rubio did not immediately comment after the meeting. Trump, meanwhile, told reporters in the Oval Office: “We need Greenland for national security.”

“The problem is there’s not a thing that Denmark can do about it if Russia or China wants to occupy Greenland, but there’s everything we can do,” he said, adding that he does not believe the US can rely on Denmark to defend the island.

The talks came as allies in Europe moved quickly to show support for Greenland.

Sweden on Wednesday pledged to send armed forces to the territory at Denmark’s request. France’s foreign minister said the country planned to open a consulate on the island next month.

Germany said in a statement provided to the BBC that it would send a “reconnaissance team” to Greenland to “explore the general conditions for possible military contributions to support Denmark in ensuring security in the region”.

Denmark said its military expansion in Greenland will take place “in close co-operation with allies”.

“Geopolitical tensions have spread to the arctic,” it said in a statement.

The White House talks were just the latest round of diplomatic discussions over Trump’s growing interest in the territory.

It is unclear whether the president is considering using military force to seize the island, and he once again declined to rule it out when asked on Wednesday.

Other options reportedly under consideration include purchasing the territory – though neither Danes nor Greenlanders have said it is for sale.

Since taking office, Vance has criticised Denmark’s stewardship of Greenland. The vice president visited soon after taking office.

Trump has argued control of the territory is critical for his planned missile defence system, Golden Dome.

“It is vital for the Golden Dome that we are building,” Trump said in a social media post early on Wednesday. “NATO should be leading the way for us to get it.”

Public opinion polls suggest a majority of Greenland residents oppose coming under US control.

Most Americans oppose US control of Greenland as well. A Reuters/Ipsos poll released Wednesday indicated that just 17% of Americans support the US seizing Greenland, compared to 47 percent who said they opposed Trump’s push to acquire the island.

The latest talks on Greenland follow US military operations in Venezuela and against ISIS targets in Syria. Trump has also threatened to take military action to stop Iran’s crackdown on a growing protest movement engulfing the nation.