It would be the end of NATO if the US took Greenland by force and European Union member states are under obligation to come to Denmark's assistance if it was faced with military aggression, the European Commissioner for Defence and Space said on Monday.

Trump has said the US must own Greenland, an autonomous part of the Kingdom of Denmark, to prevent Russia or China occupying the strategically located and minerals-rich Arctic territory, arguing US military presence there was not enough.

Both Greenland and Denmark have said that Greenland is not for sale but Trump has not ruled out taking it by force.

"I agree with the Danish Prime Minister that it will be the end of NATO, but also among people it will be also very, very negative," Commissioner Andrius Kubilius told Reuters at a security conference in Sweden.

Kubilius also said that the European Union Treaty article 42.7 obliged member states to come to Denmark's assistance if faced with military aggression.

"It will depend on very much on Denmark, how they will react, what will be their position, but definitely there is such an obligation of member sates to come for mutual assistance if another member state is facing military aggression," he said.