The Kremlin said on Monday that Russian President Vladimir Putin has been invited to join US President Donald Trump's "Board of Peace", and that Moscow is studying the proposal and hopes for contacts with Washington concerning it.

On the other hand, it also said that it was hard to disagree with experts who said that Trump would go down in the history of the United States and the world if he took control of Greenland.

Kremlin spokesman Dmitry Peskov said he was not discussing whether such a step would be good or bad - simply stating a fact.

Trump has repeatedly insisted he will settle for nothing less than ownership of Greenland, an autonomous territory of Denmark. He has said that if the United States does not take control of Greenland, then Russia or China will.

When asked to comment on Trump's remarks about the alleged Russian threat, Peskov said that there has been a lot of "disturbing information" lately but that the Kremlin would not comment on the alleged Russian designs on Greenland.

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"Here, perhaps, it is possible to abstract from whether this is good or bad, whether it will comply with the parameters of international law or not," Peskov said.

"There are international experts who believe that by resolving the issue of Greenland's incorporation, Trump will certainly go down in history. And not only in the history of the United States, but also in world history."

Leaders of both Denmark and Greenland have insisted the island is not for sale and does not want to be part of the United States.

Russia's foreign ministry last week said that it was unacceptable for the West to keep claiming that Russia and China threatened Greenland, and said the crisis over the territory showed the double-standards of Western powers which claimed moral superiority.