Denmark's Prime Minister Mette Frederiksen says Europe won't be blackmailed, as she and other European leaders continue to weigh their response to US President Donald Trump's tariff threats over Greenland.

Trump says he will impose new taxes on eight US allies - Denmark, Finland, France, Germany, the Netherlands, Norway, Sweden and the UK - in February if they oppose his proposed takeover of the autonomous Danish territory.

He insists Greenland is critical for US security and has not ruled out taking it by force - a move that has drawn widespread criticism.

The countries threatened with tariffs have now issued a joint statement, saying Trump's plan risks a dangerous downward spiral.

Tariff threats undermine transatlantic relations, they said, reiterating that they stand in full solidarity with the Kingdom of Denmark and the people of Greenland.

The countries stressed they are committed to strengthening Arctic security as a shared transatlantic interest as members of the NATO military alliance.

Separately, Frederiksen wrote on Facebook: We want to cooperate and we are not the ones seeking conflict. And I am happy for the consistent messages from the rest of the continent: Europe will not be blackmailed.

It is all the more important that we stand firm on the fundamental values that created the European community.

The comments come as EU members held an emergency meeting in Brussels on Sunday.

Trump has threatened to impose a 10% tariff on goods from Denmark, Norway, Sweden, France, Germany, the UK, the Netherlands and Finland, which would come into force on 1 February, but could later rise to 25% - and would last until a deal was reached.

Public anger in both Denmark and Greenland at Trump's threats over Greenland appears undiminished. Demonstrations against Trump's takeover plans were held in Greenland's capital, Nuuk, as well as in Danish cities.

The head of NATO, Mark Rutte, meanwhile, said he had spoken to Trump regarding the security situation in Greenland and the Arctic. We will continue working on this, and I look forward to seeing him in Davos later this week, he added.