After months of threats, retorts and closed-door negotiations, the United States has reached a deal to expand its security presence in Greenland, the semiautonomous Danish territory, according to President Trump.

The specifics of the agreement, announced on Friday, were not immediately made public. But it clearly falls short of the outright American takeover that Mr. Trump had demanded, a threat that roiled the NATO alliance, of which Denmark is a member.

In a social media post, Mr. Trump said the deal gave the United States “permanent control over security, and all other needs” in Greenland. But the Danish prime minister, Mette Frederiksen, stressed that the agreement “recognizes the sovereignty and territorial integrity” of Denmark.

Mr. Trump had said since his first term that the United States wanted to acquire Greenland, and he became more insistent about it after returning to office last year. One of his aides said Mr. Trump wanted to buy the island, and another suggested that the United States could simply take it by force.

The leaders of Greenland and Denmark rejected such ideas, and European leaders grappled with how to respond to the threat to seize territory from a NATO ally. In the end, negotiators from the United States, Greenland and Denmark met in Washington for high-stakes talks.

Here’s what you need to know:

• What’s in the deal?
• Why does Trump say he wants Greenland?
• Who controls Greenland?

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