"The EU will continue to uphold the principles of national sovereignty, territorial integrity and the inviolability of borders," EU foreign policy spokesperson Anitta Hipper told reporters.

"These are universal principles, and we will not stop defending them, all the more so if the territorial integrity of a member state of the European Union is questioned," she added.

Washington's military intervention in Venezuela has reignited fears for Greenland, which Trump has repeatedly said he wants to annex, given its strategic location in the Arctic.

While aboard Air Force One en route to Washington, Trump reiterated the goal. 

"We need Greenland from the standpoint of national security, and Denmark is not going to be able to do it," he said in response to a reporter's question.

"We'll worry about Greenland in about two months... let's talk about Greenland in 20 days."

Denmark's prime minister warned on January 5 that any US move to take Greenland by force would destroy 80 years of transatlantic security links.

Mette Frederiksen told the TV2 network: "If the United States decides to military attack another NATO country, then everything would stop -- that includes NATO and therefore post-World War II security."