An attack by the United States on a Nato ally would mean the end of both the military alliance and “post-second world war security”, Denmark’s leader has warned, after Donald Trump threatened again to take over Greenland.

Fresh from his military operation in Venezuela, the US president said on Sunday the US needed Greenland “very badly” – renewing fears of a US invasion of the largely autonomous island, which is a former Danish colony and remains part of the Danish kingdom. Greenland’s foreign and security policy continues to be controlled by Copenhagen.

Mette Frederiksen, the Danish prime minister, warned on Monday that any US attack on a Nato ally would be the end of “everything”.

“If the United States decides to militarily attack another Nato country, then everything would stop – that includes Nato and therefore post-second world war security,” Frederiksen told Danish television network TV2.

Her comments came after Greenland’s prime minister, Jens-Frederik Nielsen, made a bracingly direct statement in which he urged Trump to give up his “fantasies about annexation” and accused the US of “completely and utterly unacceptable” rhetoric, declaring: “Enough is enough.”

“Threats, pressure and talk of annexation have no place between friends,” said Nielsen in a social media post. “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.”