Denmark will not give up Greenland to the US, Danish Prime Minister Mette Frederiksen has said during an official visit to the Arctic Island.

Responding to repeated threats from Donald Trump, Frederiksen offered closer collaboration on security but told the US president: "You can't annex other countries."

Frederiksen stood alongside Greenland's Prime Minister Jens-Frederik Nielsen and his predecessor Mute Egede in a show of support and unity in the face of US threats on Thursday.

Her three-day trip to the territory follows last week's controversial visit by a US delegation headed up by Vice-President JD Vance, which was widely criticised in both Greenland and Denmark.

During his whirlwind trip, Vance reiterated Trump's ambitions to bring Greenland under United States' control for security reasons, criticised Denmark for not spending more on security in the region, and claimed it had "not done a good job" for Greenlanders.

On Thursday, US Secretary of State Marco Rubio met Danish Foreign Minister Lars Lokke Rasmussen in Brussels, where he "reaffirmed the strong relationship" between the US and Denmark, the US State Department said in a statement.

Rasmussen said Rubio had acknowledged Greenland's right to self-determination but added that Denmark would object to "any claims on Greenland", Reuters news agency reported.

After arriving in Greenland on Wednesday, Frederiksen said: "It is clear that with the pressure put on Greenland by the Americans, in terms of sovereignty, borders and the future, we need to stay united."

Frederiksen said on Thursday that Denmark was fortifying its military presence in the Arctic and offered closer collaboration with the United States in defending the region.

But she added: "When you demand to take over a part of... Denmark's territory, when we are met by pressure and by threats from our closest ally, what are we to believe in, about the country that we have admired for so many years?"

Frederiksen rode around the capital Nuuk in a Danish navy patrol boat, alongside Egede and Nielsen.

According to Danish public broadcaster DR, many people cheered at seeing the Danish prime minister, with one resident shouting from a window: "Hey Mette! Thanks for being here."

Egede, who served as prime minister for almost four years, said the island had cooperated with the US on security for almost 80 years - including the construction of the Pituffik Space Base following a 1951 agreement between Denmark and the United States.

The former leader insisted Greenland was not for sale, but added the island wanted trade with the US, Greenlandic national newspaper Sermitsiaq reported.

Trump first floated the idea of buying Greenland during his first term - and his desire to own the island has only grown with time.

Mikaela Engell, an expert on the Arctic territory who previously served as Denmark's High Commissioner to Greenland, told AFP news agency "it's very, very important and it's very reassuring for Greenlanders to see a Danish head of government."

Greenland - the world's biggest island, between the Arctic and Atlantic Oceans - has been controlled by Denmark, nearly 3,000km (1,860 miles) away, for about 300 years.

Greenland governs its own domestic affairs, but decisions on foreign and defence policy are made in Copenhagen.

Five of the six main parties favour independence from Copenhagen, but disagree over the pace with which to reach it.

A new Greenland coalition government was formed in March, led by the centre-right Democrats party which favours a gradual approach to independence.

Polls show that the vast majority of Greenlanders also want to become independent from Denmark, but do not wish to become part of the US.

Since 2009, Greenland has had the right to call an independence referendum, though in recent years some political parties have begun pushing more for one.