The US ambassador to the UN, Mike Waltz, however, said Denmark "just doesn't have the resources or the capacity to do what needs to be done in the northern region".
He told Fox News the life of Greenlanders would be "safer, stronger and more prosperous under the umbrella of the United States".
Trump has often mused that "tariff" is his favourite word, and he has made clear that he views it as something of a blunt instrument with which to convince – or coerce – countries around the world to align their policies with the desired outcomes of the White House.
But his announcement represents a significant escalation in his recently rekindled drive to acquire Greenland, despite their opposition.
It is unclear what immediately prompted the tariffs announcement, which Trump first hinted at while speaking to reporters at the White House on Friday.
While in recent weeks he has repeatedly said that a variety of options – including the potential use of military force – remained on the table, the announcement comes just days after US and Danish officials agreed to set up a high-level working group to discuss the future of the island.
In Washington's diplomatic and political circles, that announcement was seen by many as a "best-case" scenario for Denmark and its European allies – one that would, at the very least, delay any decision or further escalation from the White House.
Instead, the latest tariffs have injected a newfound sense of urgency into the issue and strained relations with important Nato allies and trading partners.
Opinion polls suggest 85% of Greenlanders oppose the territory joining the US.
Demonstrations against Trump's takeover plans were held in Danish cities as well as in Greenland's capital, Nuuk, on Saturday - before the tariff announcement.
In the Danish capital, Copenhagen, placards were held up reading: "Hands Off Greenland" and "Greenland for Greenlanders".