Trump has signalled that he wants the Arctic island -- which is believed to hold large untapped mineral and oil reserves -- to become part of the United States.
Despite Trump's fiery rhetoric over the possible use of force or tariffs to annex the Danish autonomous territory, "I have no reason to believe that there is a military threat to Greenland or Denmark," Frederiksen told Danish media before a meeting with NATO Secretary General Mark Rutte in Brussels.
That meeting followed talks earlier in the day in Berlin and Paris.
Following a meeting with French President Emmanuel Macron, the Danish head of government told reporters she had received "a great deal of support".
"This is a very, very clear message... that of course there must be respect for territory and the sovereignty of states," Frederiksen said.
Trump has talked for years about a possible deal to take control of the Danish autonomous territory.
On Saturday, he told reporters he believed that the United States would "get Greenland", which is located between the United States and Europe in a region of increasing strategic value as the melting of Arctic sea ice opens up new shipping routes.
Trump argues his country needs Greenland for "international security".
But Denmark's Foreign Minister Lars Lokke Rasmussen on Tuesday retorted that "Trump will not have Greenland".
"The Greenlandic people are a people, also in the sense of international law," Lokke told reporters.
German Chancellor Olaf Scholz, who met with Frederiksen early Tuesday in Berlin, stressed that "borders must not be moved by force".
The chancellor said "the times we live in are challenging" and require a strong Europe and NATO.
- 'Gravity of the situation' -
Tuesday's visits followed a weekend Nordic summit where leaders all "shared the gravity of the situation", Frederiksen said.
Denmark on Monday announced that it would spend 14.6 billion kroner ($2 billion) to bolster security in the Arctic.
It said it would send three new frigates to the region, as well as long-distance drones equipped with advanced imaging capabilities. It would also reinforce its satellite capabilities.
Officials in Greenland, which depends heavily on Denmark for subsidies, have long been pushing for independence but have said they are open to doing business with the United States.
A day after Trump was sworn in as president, Greenland Prime Minister Mute Egede insisted that Greenlanders "don't want to be American".
In mid-January, Frederiksen reportedly spoke to Trump by telephone, stressing that it was up to Greenland to determine its future.
According to European sources cited by the Financial Times, Danish officials described the conversation as "horrendous", and that Trump's interest in Greenland was "serious, and potentially very dangerous".
The US president, who has not ruled out a possible military intervention to annex the island, reportedly threatened Denmark with tariffs over the issue.
The United States is the small Scandinavian country's main export market.
- 'Worrying time' -
Greenland's trade and justice minister Naaja Nathanielsen on Monday told AFP that the Greenlandic people were living through a "worrying time" and were "concerned" about Trump's statements.
Nathanielsen said that the United States had had a military presence on the island for 80 years and that Greenland was "not opposed to that".
But, if Trump's intentions were for "expansionism, we are a democracy, we are allies and we ask our allies to respect our institutions".
The European Union's top military official on Saturday said that troops from EU countries could be based in Greenland.
"In my view, it would make perfect sense not only to station US forces in Greenland, as is currently the case, but also to consider stationing EU soldiers there," Robert Brieger, chairman of the European Union Military Committee told German newspaper Welt am Sonntag.
France's Foreign Minister Jean-Noel Barrot also did not rule out the possibility of European troops in Greenland.
"Why not, since it is a matter of security," Barrot told Sud Radio on Tuesday.
He stressed, however, that "that is not the wish expressed by Denmark, but it is a possibility".
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