While the prospect of conflict among NATO allies over the vast Arctic island, which is part of the Kingdom of Denmark, has receded in recent weeks, Frederiksen said the crisis was not over.
"I think the desire from the US president is exactly the same. He is very serious about this theme," she said while speaking on a panel at the Munich Security Conference on Saturday.
The panel's moderator asked the prime minister if there was a price at which Denmark would be willing to sell Greenland to Trump.
"Of course not," she responded.
"Can you put a price on a part of Spain? Or a part of the US?"
"We have to protect sovereign states. We have to protect people's right to self-determination. And the Greenlandic people have been very clear: they don't want to become Americans."
She said she supported an increased NATO presence in Greenland to safeguard the Arctic, one of the main reasons Trump has given for seeking US control of the resource-rich island.
At a meeting in Davos, Switzerland last month Trump withdrew his threats to use military force to acquire Greenland and also dropped punitive tariffs against several European countries that had opposed his efforts.
The US, Denmark and Greenland have been holding talks on the future of the island in various formats, including at the Munich conference.
Frederiksen also urged NATO partners to make a long-term commitment to the alliance's new Arctic Sentry mission, saying it must be strengthened beyond its initial launch.
The surveillance operation is intended to ensure a stronger presence of the alliance in the region. Frederiksen said that her country had been requesting a permanent NATO presence on Greenland for years.
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