Even though many Greenlanders said they are not fans of Mr. Trump, they enjoy watching him push Denmark around. In interviews, they expressed confidence that this would ultimately help them get a sovereign state of their own — something no other Inuit community has achieved — unless America swallows them first.

“Everyone I know is saying, ‘This is all so hilarious, it’s all so absurd, but it’s also so nice,’” said Svend Hardenberg, a mining executive and, more recently, a star in a hot Danish Netflix series that, serendipitously, had a whole season about Greenland.

“There’s going to be a lot of people trying to sway us, this way or that,” he said. “So now we have to figure how to do the best for ourselves, to really see what the U.S. and Denmark can offer.”

“This,” he added, “is our moment.”

The Political Question

One afternoon last month in Nuuk, Greenland’s capital, Kuno Fencker, a member of Parliament, marched out of a news conference, the frustration showing on his face. Greenland’s prime minister, Múte B. Egede, had ducked a question about independence, refusing to answer clearly why the government should not push for it now.

Mr. Fencker wants Greenland to start divorce negotiations with Denmark immediately.

“Why shouldn’t we be a part of the global world?” he asked. “Why are we not allowed to become members of the U.N.? Why shouldn’t we be able to be members of the international organizations regarding our fisheries, whales, everything? Why is it that a Danish guy or woman in Denmark has to decide that?”