US President Donald Trump in a written message to Norway's prime minister said he no longer feels obligated "to think purely of Peace" because he had not been awarded the Nobel Peace Prize, and he repeated his demand for control of Greenland.

The note, shared widely with other nations by the U.S. administration, was in response to a brief message to Trump from Norway's Prime Minister Jonas Gahr Stoere and Finnish President Alexander Stubb opposing his decision to impose tariffs on European allies over their refusal to let the US take control of Greenland, Stoere said in a statement.

In their message, Stoere and Stubb pointed to the need to de-escalate the rhetoric and requested a phone call with Trump, the Norwegian premier's statement said. Trump's response came only a short time after they had sent their message.

"Dear Jonas: 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," Trump wrote in his response, which was seen by Reuters.

Trump has openly campaigned for the Nobel Peace Prize, which last year was awarded to Venezuelan opposition leader Maria Corina Machado.

"I have several times explained clearly to Trump the well-known fact that it is an independent Nobel Committee, and not the Norwegian government, which awards the prize," Stoere said.

Machado gave Trump her gold medal during a White House meeting last week, though the Norwegian Nobel Committee has said the prize cannot be transferred, shared or revoked.

The Nobel Committee did not immediately reply on Monday to a request for comment.

In his message to Stoere, Trump also again questioned Danish sovereignty over Greenland, saying: "Denmark cannot protect that land from Russia or China, and why do they have a 'right of ownership' anyway?"

"There are no written documents, it's only that a boat landed there hundreds of years ago, but we had boats landing there, also."

European leaders held an emergency meeting on Sunday after US President Donald Trump threatened sweeping new tariffs on some NATO allies,

Danish sovereignty over the vast, mineral-rich island is documented in a series of binding legal instruments including a treaty agreed in 1814. The US has repeatedly recognised that Greenland is part of the Kingdom of Denmark.

Trump concluded his message to Stoere with typical ebullience.

"I have done more for NATO than any other person since its founding, and now, NATO should do something for the United States. The World is not secure unless we have Complete and Total Control of Greenland. Thank you! President DJT."