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 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.
In a sign of how tensions have increased in recent days, thousands of Greenlanders marched over the weekend in protest of any effort to take over their island.
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 that she was moved by the quick response of allies to the tariff threat and said it showed that countries realise "this is about more than Greenland".
"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, with White House deputy press secretary Anna Kelly saying that Trump "is confident Greenlanders would be better served if protected by the United States from modern threats in the Arctic region".
The Norwegian Nobel Committee is an independent body whose five members are appointed by the Norwegian Parliament.
In his latest threat of tariffs, Trump indicated the import taxes would be retaliation for last week's deployment of symbolic numbers of troops from the European countries to Greenland - though he also suggested that he was using the tariffs as leverage to negotiate with Denmark.
European governments said that the troops travelled to the island to assess Arctic security, part of a response to Trump's own concerns about interference from Russia and China.
They are now looking at setting up a more permanent military presence to help guarantee security in the Arctic region, a key demand of the United States, Swedish Defence Minister Pål Jonson said.
