An emergency order from the Venezuelan government appears to criminalize support for the U.S. attack.

President Trump has ridiculed Denmark’s dog sled teams in Greenland.He has cited mysterious Chinese and Russian ships prowling off the coast.He seems increasingly fixated on the idea that the United States should take over this gigantic icebound island, with one official saying the president wants to buy it and another suggesting that the United States could simply take it. Just a few days ago, Mr. Trump said: “We need Greenland from the standpoint of national security.”But the question is: Does the United States even need to buy Greenland — or do something more drastic — to accomplish all of Mr. Trump’s goals?Under a little-known Cold War agreement, the United States already enjoys sweeping military access in Greenland. Right now, the United States has one base in a very remote corner of the island. But the agreement allows it to “construct, install, maintain, and operate” military bases across Greenland, “house personnel” and “control landings, takeoffs, anchorages, moorings, movements, and operation of ships, aircraft, and waterborne craft.”It was signed in 1951 by the United States and Denmark, which colonized Greenland more than 300 years ago and still controls some of its affairs.“The U.S. has such a free hand in Greenland that it can pretty much do what it wants,” said Mikkel Runge Olesen, a researcher at the Danish Institute for International Studies in Copenhagen.“I have a very hard time seeing that the U.S. couldn’t get pretty much everything it wanted,” he said, adding, “if it just asked nicely.”But buying Greenland — something that Secretary of State Marco Rubio told lawmakers on Tuesday was Mr. Trump’s latest plan — is a different question.Greenland does not want to be bought by anyone — especially not the United States. And Denmark does not have the authority to sell it, Dr. Olesen said.“It is impossible,” he said.In the past, Denmark would have been the decider. In 1946, it refused the Truman administration’s offer of $100 million in gold.Today, things are different. Greenlanders now have the right to hold a referendum on independence and Danish officials have said it’s up to the island’s 57,000 inhabitants to decide their future. A poll last year found 85 percent of residents opposed the idea of an American takeover.Greenland’s prime minister, Jens-Frederik Nielsen, has repeatedly scoffed at the idea of being bought, saying this past week, “Our country is not for sale.”The relatively short, straightforward defense agreement between the United States and Denmark was updated in 2004 to include Greenland’s semiautonomous government, giving it a say in how American military operations might affect the local population. The roots of the agreement go back to a partnership forged during World War II.At that time, Denmark was occupied by the Nazis. Its ambassador in Washington, cut off from Copenhagen, took it upon himself to strike a defense agreement for Greenland with the United States. (The island is part of North America, along the Arctic Ocean and close to Canada’s coast.)ImageA former American air base in Kangerlussuaq in western Greenland. Under a little-known Cold War agreement, the United States has sweeping military access in Greenland.The fear was that Nazis could use Greenland as a steppingstone to America. The Germans had already established small meteorological bases on the island’s east coast and relayed information for battles in Europe. American troops eventually ousted them and established more than a dozen bases there with thousands of troops, landing strips and other military facilities.After World War II, the United States continued to run some bases and a string of early warning radar sites. As the Cold War wound down, the United States closed all of them except one. It’s now called the Pittufik Space Base and helps track missiles crossing the North Pole.The Danes have a light presence, too: a few hundred troops, including special forces that use dog sleds to conduct long-range patrols. In recent months, the Danish government has vowed to upgrade its bases and increase surveillance.After American special forces captured Nicolás Maduro, the ousted president of Venezuela, from a safehouse last week, Mr. Trump seemed emboldened. Stephen Miller, a top aide, then claimed that Greenland should belong to the United States and that “nobody’s going to fight the United States” over it. Danish and Greenlandic anxiety skyrocketed.On Tuesday night, Danish and Greenlandic leaders asked to meet with Mr. Rubio, according to Greenland’s foreign minister. It’s not clear if or when that might happen.Tensions between Mr. Trump and Denmark’s prime minister, Mette Frederiksen, have been steadily rising, as Mr. Trump pushes to “get” Greenland, as he puts it, while Ms. Frederiksen refuses to kowtow to him.Just a few days ago, Ms. Frederiksen cited the 1951 agreement, saying, “We already have a defense agreement between the Kingdom and the United States today, which gives the United States wide access to Greenland.” She urged the United States “to stop the threats” and said an American attack on Greenland would mean the end of the international world order.European leaders issued their own statement on Tuesday, also citing the 1951 agreement and saying, “Greenland belongs to its people.”ImageAn American built, Cold War-era satellite station, referred to locally as Mickey Mouse, remains on a hill above Kangerlussuaq.Credit...Ivor Prickett for The New York TimesAnalysts said that if the United States tried to use the defense pact as a fig leaf to send in a lot of troops and try to occupy Greenland, that wouldn’t be legal either.According to the 2004 amendment, the United States is supposed to consult with Denmark and Greenland before it makes “any significant changes” in its military operations on the island. The 2004 amendment, which was signed by Gen. Colin L. Powell, who was then the secretary of state, explicitly recognizes Greenland as “an equal part of the Kingdom of Denmark.”Peter Ernstved Rasmussen, a Danish defense analyst, said that in practice, if American forces made reasonable requests, “the U.S. would always get a yes.”“It is a courtesy formula,” he said. “If the U.S. wanted to act without asking, it could simply inform Denmark that it is building a base, an airfield or a port.”That’s what infuriates longtime Danish political experts. If Mr. Trump wanted to beef up Greenland’s security right now, he could. But there has been no such official American request, said Jens Adser Sorensen, a former senior official in Denmark’s parliament.“Why don’t you use the mechanism of the defense agreement if you’re so worried about the security situation?” he said, adding, “The framework is there. It’s in place.”But Greenland’s strategic location is not the only thing that’s attracted Mr. Trump’s inner circle. The enormous island has another draw: critical minerals, loads of them, buried under the ice. Here, too, analysts say, the United States doesn’t need to take over the island to get them.Greenlanders have said they are open to doing business — with just about anyone.