"Trump will not have Greenland. Greenland is Greenland. And the Greenlandic people are a people, also in the sense of international law," Rasmussen told reporters, adding that "this is also why we have said time and again that it is ultimately Greenland that decides Greenland's situation."
Rasmussen's comments came as Prime Minister Mette Frederiksen travelled across Europe on Tuesday in what appeared an attempt to shore up support from allies amid Trump's increasingly aggressive pursuit of the Arctic territory, an autonomous part of the Danish kingdom..
Frederiksen said she had received support from European leaders to counter Trump's threats to take over Greenland.
After an initial stopover in Berlin in the morning, Frederiksen was in Paris by midday and due to travel to Brussels in the afternoon to meet NATO Secretary General Mark Rutte.
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.
"This is a crucial part of the international community, the international community that we have built together since World War II," she added.
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.
The US president told reporters on Saturday he believed the US would "get Greenland", which he has insisted his country needs for "international security".
"I think Greenland will be worked out with us, I think we're going to have it. I think the people want to be with us. As you know, there's 55,000 people there. They want to be with us," Trump said according to media including CNBC and Forbes.
Greenland’s premier Múte Egede last week reiterated that Greenland does not want to become American, while Frederiksen has repeatedly stated Greenland’s future can only be decided by Greenland.
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Frederiksen met earlier on Tuesday with German Chancellor Olaf Scholz in Berlin.
After speaking about Russia's war in Ukraine, Scholz stressed that "borders must not be moved by force" and added the English-language phrase: "To whom it may concern."
The chancellor said "the times we live in are challenging" and require a strong Europe and NATO. He stressed that "Denmark and Germany are strong partners and close friends".
'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 US.
A day after Trump was sworn in as president, Greenland's PM Egede insisted that Greenlanders "don't want to be American".
READ ALSO: Greenlanders living in 'worrying time' amid Trump aggression
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 excluded 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.
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