Greenland may become independent if its residents want, but is unlikely to become a U.S. state, Denmark's foreign minister said on Wednesday after U.S. President-elect Donald Trump refused to rule out force to take control of the Arctic island.

Greenland's leader met with the Danish king in Copenhagen on Wednesday, a day after Trump's remarks thrust the fate of the mineral-rich and strategically important island, which is under Danish rule, to the top of world headlines.

Trump, who takes office on Jan. 20, said on Tuesday he would not rule out using military or economic action to make Greenland part of the United States. The same day, Trump's eldest son, Donald Trump Jr., made a private visit to Greenland.