Lars Lokke Rasmussen,(L), and Greenland`s foreign minister, Vivian Motzfeldt, during a news conference at the Danish Embassy, in Washington, D.C., on Wednesday. (Photo by AP)

High-level talks over the future of Greenland have ended in disagreement as the US President Donald Trump reiterates the "need" to seize control of the territory amid rising tensions with European allies.

The meeting, which took place in Washington on Wednesday, involved US Vice President JD Vance, Secretary of State Marco Rubio, Danish Foreign Minister Lars Rasmussen, and Greenlandic Foreign Minister Vivian Motzfeldt.

However, the talks ended without a resolution, with Rasmussen stating that the sides had "agreed to disagree."

"We have decided to form a high-level working group to explore if we can find a common way forward," Rasmussen said

"The group, in our view, should focus on how to address the American security concerns, while at the same time respecting the red lines of the Kingdom of Denmark," he added.

Trump doubled down on his stance after the talks, "Greenland is very important for the national security, including of Denmark," Trump said. "And 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. You found that out last week with Venezuela."

Trump`s remarks follow an illegal US military aggression in Venezuela earlier this month, in which US forces kidnapped Venezuelan President Nicolás Maduro and his wife Cilia Flores.

Rasmussen insisted that a US takeover of Greenland as suggested by Trump is "totally unacceptable".

Meanwhile, Sweden, France and Norway have begun sending armed forces to Greenland at Denmark`s request.

Denmark is also increasing its presence and will send additional aircraft, ships and soldiers to the island as part of an ongoing effort to strengthen NATO`s presence in the Arctic.

Earlier in the day, Rasmussen said Denmark shared Trump`s concerns that there was a changing security environment in the Arctic and the country wanted to work with the US to counter threats.

"The big difference is whether that must lead to a situation where the US acquires Greenland, and that is absolutely not necessary," he emphasized.

The meeting with the top White House officials was arranged after Trump reiterated that the US "needs" total control of the island, hinting he could take it by force if other ways fail. Trump has suggested paying Greenlanders large sums of money to accept to join the US.

Meanwhile, Greenlanders reacted to the high-level talks over the future of Greenland in Washington saying they felt relieved that the meeting did not end in a shouting match.

"We have this concern that it could be a kind of [Ukrainian President Volodymyr] Zelensky meeting," said Nuuk resident Peter Jensen, referencing a heated, live-broadcast meeting between the Ukrainian leader, Trump and Vance last year. "So I`m happy that it was a meeting without press because it would have escalated what the Americans want to have."