New Delhi, Jan. 13 -- President Donald Trump's repeated threats to seize control of Greenland are straining relations with U.S. allies in NATO and have sparked a warning that doing so by force could spell the end of the world's biggest security alliance.

Tensions have routinely spiked among some of NATO's members over the decades, notably between neighbors Greece and Turkey. But it would set a dangerous precedent should its most powerful country, the United States, annex the territory of another ally.

"One way or the other, we're going to have Greenland," Trump reaffirmed on Sunday. The White House has not ruled out the use of military force. Trump said he wants to prevent Russia or China from taking over and that making a deal would be...