Keir Starmer has publicly backed the Danish prime minister over Donald Trump after she demanded that the US stop its threats to forcibly take over Greenland.

Speaking after Mike Tapp, the migration minister, repeatedly dodged questions about threats by Trump and his allies to seize Greenland, Starmer told broadcasters that he supported Mette Frederiksen after she criticised US rhetoric.

“Well, I stand with her, and she’s right about the future of Greenland,” Starmer told Sky News.

Asked by the BBC if he agreed with Danish calls for Trump to stop raising the idea that the US should annex the island, which is largely autonomous but remains part of the Danish kingdom, Starmer replied: “Yes.”

He went on: “Greenland and the kingdom of Denmark are to decide the future of Greenland, and only Greenland and the kingdom of Denmark.

“Denmark is a close ally in Europe, it is a Nato ally, and it’s very important the future of Greenland is, as I say, for the kingdom of Denmark, and for Greenland, and only for Greenland and the kingdom of Denmark.”

Following the US’s seizure of Nicolás Maduro, the Venezuelan president, after a military raid on the country, Trump has reiterated his desire to take Greenland, saying: “We need Greenland from the standpoint of national security, and Denmark is not going to be able to do it.”

Hours after the raid in Venezuela, Katie Miller, a rightwing podcaster who is married to Stephen Miller, Trump’s deputy chief of staff for policy, on Saturday posted on X a map of Greenland draped in the stars and stripes with the caption: “SOON.”

Speaking on Sunday, Frederiksen said: “It makes absolutely no sense to talk about the US needing to take over Greenland. The US has no right to annex any of the three countries in the Danish kingdom.” The third part of the kingdom is the Faroe Islands.

Greenland’s prime minister, Jens-Frederik Nielsen, called Miller’s comments “disrespectful” on X, adding: “Relations between nations and peoples are built on mutual respect and international law – not on symbolic gestures that disregard our status and our rights.”

In a more outspoken post on Monday, he wrote: “Threats, pressure and talk of annexation have no place between friends.

“That is not how you speak to a people who have shown responsibility, stability and loyalty time and again. Enough is enough. No more pressure. No more innuendo. No more fantasies about annexation.”

Greenland, he said, was “open to dialogue” but it had to come through the appropriate channels and in line with international law, “not random and disrespectful posts on social media”.

He added: “Greenland is our home and our territory. And that is how it will remain.”

In broadcast interviews earlier on Monday, Tapp refused to directly criticise the idea of a US takeover of Greenland, telling Sky News: “Diplomacy is delicate, which means we’re not here to give a running commentary in the news.”