Copenhagen, Denmark - Greenland will never be a "piece of property" to be bought, the Arctic island's new prime minister said on Sunday, criticizing US talk of seizing the Danish autonomous territory as lacking respect.

Jens-Frederik Nielsen made the comments as he paid his first visit to Denmark since taking office, with US President Donald Trump's repeated threats to take his strategically located island looming large over the diplomatic trip.

"We will never, ever be a piece of property that can be bought by anyone, and that's the message I think is most important to understand," Nielsen told reporters alongside Danish Prime Minister Mette Frederiksen.

His visit follows one by Frederiksen to Greenland in early April, when she told the US "you cannot annex another country."

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Both Frederiksen and Nielsen, who leads Greenland's new coalition government after his center-right Democrats party won a legislative election in March, said they would be willing to meet the US leader for talks.

Tensions between the US and Denmark have soared after Trump repeatedly said he wanted to take control of the resource-rich Arctic island.

The US president has insisted Washington needs control of Greenland for security reasons, refusing to rule out the use of force to secure it.

"I think we need that for international peace, and if we don't have that it's a big threat to our world. So I think Greenland is very important for international peace," Trump told reporters Thursday during a press conference alongside Norwegian Prime Minister Jonas Gahr Store.

"We are in a situation now where we need to stand together. The talk from the United States has not been respectful," said Nielsen.

"I totally agree with that," Frederiksen added.

Nielsen reiterated that Greenland was ready to deepen ties with the US.

"We are ready for a strong partnership, we are ready for more development, but we want respect," he said. "You cannot have a partner where there is no mutual respect."