"Greenland is a democratic society with the right to make its own decisions," Nielsen wrote on Facebook.
"The latest statements from the US, including threats of tariffs, do not change that line. We will not let ourselves be pressured. We stand firm on dialogue, on respect and on international law."
Nielsen also expressed gratitude to the thousands of people who demonstrated in support of Greenland on Saturday in both Denmark and the Arctic territory.
"The demonstrations here at home and in Denmark have shown a strong and dignified unity. Many people have peacefully expressed love for our country and respect for our democracy. I am very grateful for that," he said.
He further highlighted the importance of a meeting in Brussels on Monday between Danish Defence Minister Troels Lund Poulsen and Greenland's Foreign Minister Vivian Motzfeldt with NATO Secretary General Mark Rutte.
Denmark and Greenland discussed the possibility of having a NATO mission in Greenland and the Arctic, Poulsen said after the meeting.
"We have proposed this. The NATO Secretary General has also taken note of this, and I believe we can now hopefully establish a framework for how this can be achieved," Poulsen said.
Poulsen said that the United States is important for European security.
"There are many things that Europe cannot do on its own," he said.
He added: "But some comments coming from the US president cause great pain."
US President Donald Trump threatened on Saturday to impose tariffs on eight European countries that have announced the deployment of troops to Greenland.
Those countries are Germany, Finland, France, the Netherlands, Norway, Sweden and the United Kingdom in addition to Denmark.
Trump added that the measures would remain in place until an agreement is reached for the "full and total purchase of Greenland" by the US.
"We'll continue to work together as Allies on these important issues," NATO chief Rutte said on X.
On Monday, Danish broadcaster TV2 reported on the basis of Defence Ministry information that Denmark would send more combat troops to Greenland.
While the precise number was unknown, it was reported to be a "considerable contribution," the broadcaster said.
TV2 said the new troops would arrive at Kangerlussuaq, 300km to the north of the island's capital at Nuuk on Monday.
Army chief Major General Peter Boysen would accompany the deployment, the report said.
The Norwegian government confirmed on Monday that Prime Minister Jonas Gahr Støre had received a message from Trump about Greenland.
The message read in part: "Considering your Country decided not to give me the Nobel Peace Prize for having stopped 8 Wars PLUS, I no longer feel an obligation to think purely of Peace, although it will always be predominant, but can now think about what is good and proper for the United States of America".
It concluded: "The World is not secure unless we have Complete and Total Control of Greenland."
The Norwegian leader said Trump's message was a reply to an earlier missive sent on behalf of himself and Finnish President Alexander Stubb in which they conveyed their opposition to the tariff announcement, pointed to a need to de-escalate and proposed a telephone conversation among the three leaders.
He told TV2 Norway that he had not responded to the message but "I still believe it's wise to talk," and he hopes to talk with Trump at the World Economic Forum in Davos this week.
US Treasury Secretary Scott Bessent defended Trump's approach in Greenland in comments to reporters in Davos.
"I think it's a complete canard that the president would be doing this because of the Nobel," Bessent said.
Bessent insisted Trump "is looking at Greenland as a strategic asset for the United States," adding that "we are not going to outsource our hemispheric security to anyone else".
with Reuters, AP and EFE
