Frederiksen told media in Copenhagen on Wednesday that she was “disappointed and surprised” by Trump’s decision to cancel his state visit, which the US president announced on Twitter.
Trump later sniped at Denmark's premier over his desire to buy the icy autonomous territory, saying her blunt refusal to consider any negotiation was "nasty."
The US president told reporters he had taken offence at Frederiksen's description of any such deal as "absurd."
"It was not a nice way of doing it. She could have just said no, we'd rather not do it," Trump said. "She's not talking to me, she's talking to the United States of America."
That assessment did not appear to take into account Trump’s public, unsolicited and unilateral discussion of his interest in buying Greenland, which forced Frederiksen into a response.
But the PM refused to enter into a war of words with her American counterpart.
“I think we should keep in mind that it is the American president who is cancelling (the state visit),” Frederiksen told TV2.
“I won’t hide the fact that many people in Greenland think this discussion about a sale has been difficult, and [Greenland autonomous government leader] Kim Kielsen has made it very clear that Greenland is not for sale, and I support that,” she said.
During a visit to Greenland last week, Frederiksen said that “thankfully, the time where you buy and sell other countries and populations is over. Let’s leave it there.”
She also called the prospect of Denmark selling the autonomous territory an “absurd discussion”.
Asked whether she would use the word ‘absurd’ again, she straight-batted the question.
“I’m not going to get into a war of words with anyone, including the American president, and Kim Kielsen has made it clear Greenland is not for sale and I support that,” she said.
In comments given to media on Wednesday, Frederiksen stressed the ongoing importance of the relationship between the two countries, and also said she did not expect the episode to have any lasting effect on "trade or security-related questions".
“The United States is one of our closest and most important allies and we have many shared interests which we would have liked to discuss during the visit,” she said.
“Possibilities and challenges” related to the Arctic region would have been one of the areas to be discussed, the PM said.
“Our desire for a more strategic and stronger relationship with the USA with regard to the Arctic remains completely unaltered, and as such, our invitation for a stronger strategic partnership with the Americans is still open,” she added.