Karol Nawrocki made the appeal at a news conference in Davos on Thursday.
Asked if US President Donald Trump's declaration he would not use force to take Greenland had reassured him, Nawrocki said he had not needed to be reassured.
He said: "We've all taken part in an unnecessary ramping up of emotions, also in Europe, where NATO soldiers from the EU visited Greenland."
The president said he had not "felt there was any threat of a conflict among NATO allies over Greenland at a time when there are so many threats around the world."
Nawrocki said Trump's speech at Davos offered hope that the issue would be "resolved diplomatically" between Denmark and the United States, "with the participation of the people and leaders of Greenland."
He added he had been certain from the start that that would happen.
Nawrocki also said that "some of our partners in Western Europe" should refrain from "gestures of resentment towards the US that are unnecessary neither for NATO nor for the European Union."
"You won't see Poland among these countries," he said.
The US ambition to acquire Greenland was the main theme of Trump's speech in Davos on Wednesday.
The US president for the first time ruled out the use of force. He demanded negotiations on the acquisition of Greenland and warned he would "remember" if the answer was negative.
Trump later also withdrew his threat to impose 10-percent tariffs on eight European countries that sent their troops to Greenland in response to the US plan to seize the island.
The US president said that "based on a highly productive meeting with NATO Secretary-General Mark Rutte," the two had prepared the framework for a future agreement on Greenland and the Arctic region.
Trump declared that due to this, he would not slap tariffs on the eight EU countries. They were to take effect on February 1.
Trump also announced that in connection with Greenland, talks were underway on the American defence system, the so-called Golden Dome.
Meanwhile, Rutte told broadcaster Fox News his talks with Trump had not concerned the issue of Denmark's sovereignty over Greenland. He added they had agreed that the Arctic region required collective defence.
Danish Prime Minister Mette Frederiksen said on Thursday that Denmark and Greenland would continue to engage in constructive dialogue on security in the Arctic, provided it was conducted with respect for her country's territorial integrity.
(pm)
Source: PAP