N UUK, Greenland — Greenland’s likely new prime minister on Wednesday rejected U.S. President Donald Trump’s effort to take control of the island, saying Greenlanders must be allowed to decide their own future as it moves toward independence from Denmark.

In the last few months, the phenomenon of fake news has come to Greenland. Ads posted on Facebook, Greenland’s main social network, variously suggested that two prominent politicians had either been sued by the Bank of Greenland or physically attacked,