Germany's top diplomat on Monday played down the risk of a US attack on Greenland, after President Donald Trump's repeated threats to seize the island from Nato ally Denmark.

Asked after meeting Secretary of State Marco Rubio about a unilateral military move by Trump, German Foreign Minister Johann Wadephul said: "I have no indication that this is being seriously considered."

"Rather, I believe there is a common interest in addressing the security issues that arise in the Arctic region, and that we should and will do so," he told reporters.

"Nato is only now in the process of developing more concrete plans on this, and these will then be discussed jointly with our US partners."

Wadephul's visit comes ahead of talks this week in Washington between Rubio and the top diplomats of Denmark and Greenland, which is an autonomous territory of Denmark.

Trump in recent days has vowed that the United States will take Greenland "one way or the other" and said he can do it "the nice way or the more difficult way."

Greenland's government on Monday repeated that it would not accept a US takeover under "any circumstance."

Greenland and Nato also said Monday that they were working on bolstering defense of the Arctic territory, a key concern cited by Trump.

Trump has repeatedly pointed to growing Arctic activity by Russia and China as a reason why the United States needs to take over Greenland.

But he has also spoken more broadly of his desire to expand the land mass controlled by the United States. (AFP)