Trump's text message to Jonas Gahr Støre released on Monday appears to ratchet up a standoff between Washington and its closest allies over his threats to take over Greenland, a self-governing territory of NATO member Denmark.
Store issued a statement on social media platform X saying "threats have no place among allies".
On Saturday, Trump announced a 10 per cent import tax starting in February on goods from eight nations that have rallied around Denmark and Greenland, including Norway.
Those countries issued a forceful rebuke.
Many longtime allies of the US remained resolute that Greenland was not for sale but encouraged Washington to discuss solutions.
In a statement on social media, the European Union's foreign policy chief Kaja Kallas said the bloc had "no interest to pick a fight" but would "hold our ground".
The White House has not ruled taking control of the strategic Arctic island by force.
Asked whether Trump could invade Greenland, Danish Foreign Minister Lars Løkke Rasmussen said "you can't leave anything out until the president himself has decided to leave anything out".
British Prime Minister Keir Starmer also sought to de-escalate tensions.
"I think this can be resolved and should be resolved through calm discussion," he said, adding that he did not believe military action would occur.
Early on Tuesday, US time, Trump posted on social media that he had spoken with NATO Secretary General Mark Rutte.
"I agreed to a meeting of the various parties in Davos, Switzerland," he said, where leaders will be attending the World Economic Forum's annual meeting this week.
Trump also posted a text message from Emmanuel Macron in which the French president suggested a meeting of members of the Group of Seven industrialised democracies in Paris after the Davos gathering.
Later, however, Trump posted some provocatively doctored images. One showed him planting the US flag next to a sign reading "Greenland, US Territory, Est. 2026".
The other showed Trump in the Oval Office next to a map that showed Greenland and Canada covered with the US stars and stripes.
Greenland Prime Minister Jens-Frederik Nielsen said in a Facebook post on Monday the tariff threats would not change their stance.
"We will not be pressured," he wrote.
Meanwhile, Naaja Nathanielsen, Greenland's minister for business, minerals, energy, justice and equality, told The Associated Press she was moved by the quick response of allies to the tariff threat.
"I think a lot of countries are afraid that if they let Greenland go, what would be next?"
Trump's text message to Gahr Støre was released by the Norwegian government.
"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," Trump wrote.
"The World is not secure unless we have Complete and Total Control of Greenland."
The White House confirmed the authenticity of the message.
Trump has openly coveted the peace prize, which the independent Norwegian Nobel Committee awarded to Venezuelan opposition leader María Corina Machado in 2025.
Last week, Machado presented her Nobel medal to Trump, who said he planned to keep it. Trump later told reporters he didn't care about the Nobel prize.
"A very fine woman felt that I deserved it and really wanted me to have the Nobel prize. And I appreciate that.
"If anybody thinks that Norway doesn't control the Nobel prize, they're just kidding. ... And I don't care what Norway says. But I really don't care about that. What I care about is saving lives," he said.
