President Trump and his allies have reiterated that the United States wants to take over Greenland, prompting Prime Minister Mette Frederiksen of Denmark to urge him to “stop the threats” and to warn that an attack on the semiautonomous Danish territory would lead to the end of NATO.

On Sunday, Mr. Trump told reporters on Air Force One, “We need Greenland from the standpoint of national security.” The comment came as Mr. Trump seemed emboldened after the American raid that captured Venezuela’s president, Nicolás Maduro.

Stephen Miller, a key Trump aide, asserted on Monday that Greenland rightfully belonged to the United States and that Washington could take the territory if it wanted. “Nobody’s going to fight the United States militarily over the future of Greenland,” he told CNN.

Both Ms. Frederiksen and Prime Minister Jens-Frederik Nielsen of Greenland have pushed back against Mr. Trump’s campaign to take the territory.

In an interview on Monday with Danish broadcasters, Ms. Frederiksen said that a U.S. attack would have dire consequences and would lead to the end of NATO. “The international community as we know it; democratic rules of the game; NATO, the world’s strongest defensive alliance — all of that would collapse if one NATO country chose to attack another,” she said.

Mr. Nielsen said on social media that Mr. Trump’s rhetoric was “utterly unacceptable,” adding that linking the situation in Venezuela with that of Greenland was “wrong” and “disrespectful.”

Here’s what you need to know:

• Why does Trump want Greenland?
• Who controls Greenland?
• Can Trump take over Greenland?
• How strong is Denmark’s military?

Why does Trump want Greenland?

Mr. Trump says that the island is vital for American national security and that Denmark is not spending enough to safeguard it.

Greenland is important because of its geostrategic location. An American military base, specializing in missile defense, is on the island.

Most of Greenland is inside the Arctic Circle, where superpowers are vying for military and commercial dominance. Controlling the island would give Washington an outpost in an important naval corridor connecting the Atlantic Ocean and the Arctic, where climate change is melting the ice and making once unnavigable territory a theater of competition.

Greenland also has huge stores of rare-earth minerals used for making batteries, cellphones, electric vehicles and other high-tech items. Currently, China dominates the global market for the minerals.

Some scientists say that parts of Greenland’s continental shelf could hold huge oil and gas deposits. But Greenland’s government abandoned its oil ambitions in 2021, citing environmental risks and a lack of commercial viability.

Greenland has also taken legal steps to limit the potential for environmentally destructive mining practices, including a 2021 ban on uranium mining. Such measures could be overturned if the United States took over.

Who controls Greenland?

Greenland is a semiautonomous territory of Denmark, which colonized it more than 300 years ago. For centuries, Denmark governed Greenland with strict oversight, regulating commerce and allowing only limited contact with the outside world.

Greenland achieved home rule in 1979, receiving control over most internal affairs. Since 2009, Greenlanders have had the right to hold a referendum on independence.

Denmark controls Greenland’s foreign policy, defense and other areas. And the island is still largely economically dependent on Denmark: Greenland receives an annual subsidy that pays for schools, cheap gas and strong social services.

Can Trump take over Greenland?

By any measure, it would not be easy.

Last year, in an address to Congress, Mr. Trump said: “I think we’re going to get it — one way or the other.” It is not clear how he would do that.

Military intervention would rip apart the agreement that underpins NATO, of which Denmark and the United States are both founding members. But Mr. Trump has refused to rule it out. While there was a “good possibility that we could do it without military force,” he said last year, “I don’t take anything off the table.”

Mr. Trump has tried to use economic leverage to sway public opinion. In his first term, he floated the idea of buying the island.

On social media last year, he made a direct pitch to Greenlanders: “We are ready to INVEST BILLIONS OF DOLLARS to create new jobs and MAKE YOU RICH.”

But Greenland’s government moved to ban foreign and anonymous political funding in an effort “to safeguard Greenland’s political integrity.”

Greenlanders say they are happy to do business with the United States, but polls show that about 85 percent are against being absorbed.

How strong is Denmark’s military?

Denmark is a military minnow.

The United States has the most powerful military in the world with more than 1.3 million active-duty service members.

Denmark is scrambling to increase its defense capabilities and recruit more troops. A nation of six million, the country has about 16,600 uniformed employees in the military and emergency services.

Denmark has relied heavily on NATO membership for security, a dependency that has bound the country — like much of Europe — to the United States for decades.

“No one in Denmark has any kind of illusion that we should try to defend Greenland against the U.S.,” Mikkel Runge Olesen, a researcher at the Danish Institute for International Studies, a think tank, said. “It would be impossible.”