Donald Trump has again proposed annexing Greenland, after Denmark's leader urged him to "stop the threats" over the island.

Speaking to reporters, the US president said "we need Greenland from the standpoint of national security".

Trump has repeatedly raised the prospect of the semi-autonomous Danish territory becoming an annexed part of the US, citing its strategic location for defence purposes and mineral wealth.

Greenland's Prime Minister Jens Frederik Nielsen responded by saying "that's enough now" and described the notion of US control over the island as a "fantasy".

He said: "No more pressure. No more insinuations. No more fantasies of annexation. We are open to dialogue. We are open to discussions. But this must happen through the proper channels and with respect for international law."

Earlier, Denmark's Prime Minister Mette Frederiksen had said "the US has no right to annex any of the three nations in the Danish kingdom".

Frederiksen added that Denmark "and thus Greenland" was a Nato member and covered by the alliance's security guarantee, and said a defence agreement granting the US access to the island was already in place.

The Danish prime minister released her statement after Katie Miller - the wife of one of Trump's senior aides, Stephen Miller - posted on social media a map of Greenland in the colours of the American flag alongside the word "SOON".

The Danish ambassador to the US responded to the post by Miller - a right-wing podcaster and former aide to Trump during his first term - with a "friendly reminder" that the two countries were allies and saying Denmark expected respect for its territorial integrity.

The back and forth over the future Greenland comes in the wake of a major military operation against Venezuela on Saturday, seizing its president Nicolás Maduro and his wife and removing them to New York.

Trump later said the US would "run" Venezuela and US oil companies would "start making money for the country".

The situation has reignited fears that the US may consider using force to secure control of Greenland, a vast island in the Arctic - something the US president has previously refused to rule out.

Trump has claimed that making it part of the United States would serve American security interests due to its strategic location and its abundance of minerals critical to high-tech sectors.

The Trump administration's recent move to appoint a special envoy to Greenland prompted anger in Denmark.

Greenland, which has a population of 57,000 people, has had extensive self-government since 1979, though defence and foreign policy remain in Danish hands.

While most Greenlanders favour eventual independence from Denmark, opinion polls show overwhelming opposition to becoming part of the US.