With Greenland thrust into the spotlight by President Trump’s insistence that the United States will “get” the remote island at the top of the world, its parliamentary election on Tuesday took on unusual importance — not just for the outside world, but for Greenlanders.

Voter turnout was at its highest in 12 years, so much so that polling stations on the sparsely populated island, which is partly controlled by Denmark, were kept open late to accommodate long lines. Nearly 74 percent of eligible voters cast a ballot, according to official figures.

With all votes counted early Wednesday morning, the winner was Demokraatit, a party that has been critical of Mr. Trump’s rhetoric. It has taken a moderate stance on the subject of independence from Denmark, which most Greenland politicians support as a long-term goal.

But in second place was a party, Naleraq, that has pushed hard for independence sooner — which some of its members have said would enable Greenland to associate more freely with other countries, including the United States. One prominent member of Naleraq is very pro-Trump and even attended the American president’s inauguration.

Denmark colonized Greenland more than 300 years ago, and while the island is now considered a semiautonomous territory, Denmark still controls its foreign policy, defense and other aspects of its governance. Demokraatit — which won just under 30 percent of the vote, ahead of Naleraq’s 24.5 percent — has consistently argued that independence must come second to economic and social stability.