One of Donald Trump’s top aides has ramped up the pressure on Denmark by questioning Copenhagen’s claim to Greenland.

Stephen Miller, the US president’s deputy chief of staff for policy, also claimed military intervention would not be needed to take over the Arctic territory because “nobody is going to fight the United States militarily over the future of Greenland”.

Miller’s comments come amid growing tensions between the US and Denmark and Greenland after the US president’s renewed calls to take over Greenland after the removal of Venezuela’s president Nicolás Maduro.

The Danish foreign policy committee has called an extraordinary meeting of the Danish parliament on Tuesday night to discuss the Danish kingdom’s relationship with the US that will be attended by the foreign minister, Lars Løkke Rasmussen, and the defence minister, Troels Lund Poulsen.

In his interview, Miller told CNN that military intervention would not be needed in order for the US to gain control over Greenland because of its small population.

He also suggested that Denmark does not have a right to the Arctic territory, which is a former Danish colony and remains part of the Danish kingdom. Copenhagen continues to control Greenland’s foreign and security policy.

Asked whether military action against Greenland was off the table, he incorrectly stated that its population was 30,000 when in fact it is 57,000, saying: “What do you mean military action against Greenland? Greenland has a population of 30,000 people.

“The real question is what right does Denmark have to assert control over Greenland? What is the basis of their territorial claim? What is their basis of having Greenland as a colony of Denmark?”

He added: “The US is the power of Nato. For the US to secure the Arctic region to protect and defend Nato and Nato interests, obviously Greenland should be part of the US. And so that’s a conversation that we’re going to have as a country. That’s a process we’re going to have as a community of nations.”

There was, he said, “no need to even think or talk about” a military operation in Greenland, adding: “Nobody is going to fight the US militarily over the future of Greenland. That doesn’t make any sense.”

His comments came after Trump said over the weekend, fresh from his military operation in Venezuela, that the US needed Greenland “very badly”.

The Danish prime minister, Mette Frederiksen, responded on Monday by saying that an attack by the US on a Nato ally would mean the end of the military alliance and “post-second world war security”. It would, she warned, mark the end of “everything”.

Greenland’s prime minister, Jens-Frederik Nielsen, also made a strong statement in which he urged Trump to give up his “fantasies about annexation” and accused the US of “completely and utterly unacceptable” rhetoric. “Enough is enough,” he said.

Miller’s comments about Greenland came after his wife, the rightwing podcaster Katie Miller, posted a map on X of Greenland draped in a US flag with the caption “SOON” hours after the military operation in Venezuela.

Asked about his wife’s social media post, he laughed and said: “It has been the formal position of the US government since the beginning of this administration, frankly going back into the previous Trump administration, that Greenland should be part of the US. The president has been very clear about that.”

Inuit people are understood to have lived in Greenland since as early as 2500 BCE. Modern colonisation began in 1721, when Hans Egede arrived acting with the support of what was then Denmark-Norway. It remained a colony until 1953, when it became part of the kingdom of Denmark. During the second world war, when Denmark was occupied by Germany, Greenland was occupied by the US and returned to Denmark in 1945. The US has had a military base in Greenland, which is important for its ballistic missile early warning system, at Pituffik (previously Thule) since the cold war.

In recent years there has been growing support for Greenlandic independence, particularly after revelations about Denmark’s treatment of Greenlandic people – including the IUD scandal – during and since colonial rule.

But amid the spectre of Trump’s threat, Greenland in March formed a new four-party coalition government in a show of national unity, with the first page of the coalition agreement stating: “Greenland belongs to us.”