European leaders on Wednesday warned Donald Trump against threatening "sovereign borders" after the US President-elect refused to rule out military action to take Greenland.

Germany's Olaf Scholz said Trump's comments had sparked "notable incomprehension" among EU leaders the chancellor had spoken with.

Trump has designs on the mineral- and oil-rich Arctic island, an autonomous territory of European Union member Denmark that itself has eyes on independence.

He set off new alarm bells on Tuesday at a news conference when he refused to rule out military intervention over the Panama Canal and Greenland, both of which he has said he wants the United States to control.

"We need Greenland for national security purposes," he declared.

Trump also labelled the US-Canada border an "artificially drawn line" and promised to rename the Gulf of Mexico the "Gulf of America."

In Berlin, Scholz convened a press conference at short notice and stressed that the "inviolability of borders is a fundamental principle of international law."

In a later tweet in English, Scholz reiterated Berlin's position that "borders must not be moved by force" and that Trump's latest outburst had cause "uneasiness" among European governments.

Referring indirectly to Russia's war in Ukraine, Scholz said that the principle of sovereign borders "applies to every country, whether in the East or the West."

Denmark itself struck a more emollient tone, even as Trump threatened to slap high tariffs on Copenhagen if it refused to cede Greenland.

Foreign minister Lars Lokke Rasmussen said the Danish Realm – which includes Denmark, Greenland and the Faroe Islands – is "open to a dialogue with the Americans on how we can cooperate, possibly even more closely than we already do, to ensure that American ambitions are fulfilled."

French Foreign Minister Jean-Noel Barrot said Greenland was "European territory" and there was "no question of the EU letting other nations in the world, whoever they may be... attack its sovereign borders."

Greenland has been autonomous since 1979 and has its own flag, language and institutions. But justice, monetary, defence and foreign affairs all remain under Danish control. (AFP)