Nearly 40 years later, the fate of Iran’s main oil export hub, an island that Mr. Trump now calls the country’s “crown jewel,” is emerging as a pivot point in the U.S.-Israeli war on Iran.

“Just one simple word, and the pipes will be gone,” Mr. Trump said at the White House on Monday, renewing his threat to attack oil infrastructure on Kharg Island after the U.S. bombed military sites there last week. “It’ll take a long time to rebuild that.”

The tiny island, at the northern end of the Persian Gulf, presents an appealing target for a president who has often asserted that the United States should pursue oil assets when it goes to war.

An attack or a move to seize control of the island could cripple Iran’s ability to profit from its natural resources. But by taking Iranian oil off the world market — or by prompting more damaging Iranian strikes against infrastructure elsewhere in the region — Mr. Trump would risk sending energy prices even higher, with all the economic and political problems that would accompany such a surge.

Clayton Seigle, an energy specialist at the Center for Strategic and International Studies, a Washington think tank, said that Iran appeared to have refrained from attacking “the biggest oil and gas targets that would be most crippling for the world economy,” giving the country options to escalate in response to strikes on its own oil infrastructure.

And because Kharg Island is some 400 miles away from the Strait of Hormuz, even full U.S. control of the island would do little to take away Iran’s primary means of leverage against the United States: its ability to choke energy shipping out of the Persian Gulf.

Iran “already has the whole world’s energy in a stranglehold,” Mr. Seigle said. “If we take over Kharg Island today, how does that stop the Iranians from shooting at ships, shooting at critical infrastructure, and thus keeping control over the energy exports in the region?”

Mr. Trump said on social media on Friday that U.S. airstrikes had “totally obliterated” military targets on the island. The United States could attack the island’s oil infrastructure, he said, if Iran did “anything to interfere with the Free and Safe Passage of Ships through the Strait of Hormuz.” On Monday, he renewed that warning, asserting that the United States could destroy the energy facilities there “on five minutes’ notice.”

At the same time, the deployment of a unit of about 2,500 Japan-based Marines to the Middle East has added to the speculation that Mr. Trump may be tempted to try to seize the island outright. His press secretary, Karoline Leavitt, said on social media that Mr. Trump “has been remarkably consistent his entire life on Iran,” and posted the old quotation that he would “take” Kharg Island if U.S. forces were attacked.

But there would be serious risks to seizing the island, said Richard Goldberg, a senior adviser at the Foundation for Defense of Democracies, a Washington think tank with a hawkish stance on Iran.

Such an operation would only make sense, Mr. Goldberg said, if threats to U.S. forces on the island from drones or missiles were at an acceptable level, and if the United States had some control over the oil that is piped to Kharg Island.

Otherwise, Mr. Goldberg said, attacks on Kharg Island’s oil infrastructure — or, for example, the power plant that enables it — could be a means to further weaken what remains of the Iranian regime and increase the chances that a popular uprising could topple it. He argued that Iran may not have the means to retaliate more heavily against the oil assets of U.S.-friendly countries in the Gulf.

“If the end state of Epic Fury is that the regime is still there,” Mr. Goldberg said, using the name of the U.S. campaign, “then you might consider some sort of closing act that disrupts their ability to access that oil revenue.”

Military officials have declined to say what missions the Marines being sent to the Middle East would be assigned to carry out. Rather than seizing Kharg Island, they could be ordered into a different, no less dangerous mission — helping to secure the Strait of Hormuz, which their ships would need to transit before getting to the island.

Francis Galgano, an expert in military geography at Villanova University, said that he viewed an operation for Kharg Island as “perhaps more likely” than one against the coastline of the strait. Seizing Kharg Island would give the United States “an extreme pressure point on the Iranians,” he said.

“Any commitment of ground troops changes the calculus at home and abroad,” Mr. Galgano said. “It would be a huge step.”

Using U.S. troops to seize Iranian territory to protect shipping is not a new idea. Mr. Galgano was a 26-year-old Army tank captain serving in the Middle East in 1986 when Iran was attacking tankers in the Persian Gulf. He said he was involved in “war-gaming” a plan to land in Bandar Abbas, an Iranian city, to seize the Strait of Hormuz, one of many possible actions.

Of course, removing Iran’s ability to export oil from Kharg Island would mean cutting off substantial amounts of oil from the global market, possibly for a long time — a move that could send prices even higher. Oil has been hovering above $100 a barrel, up from less than $73 a barrel before the war started. At that point, some 90 percent of Iran’s crude oil exports transited through the island.

Iran has been among the few countries sending tankers through the Strait of Hormuz since the war started, meaning at least some of its oil is reaching the global market. Since March 1, at least 14 vessels laden with oil or other energy products have left Iran and passed through the narrow waterway that connects the Persian Gulf to the Gulf of Oman, according to Lloyd’s List Intelligence, a shipping analysis firm.

There are signs that Kharg Island has continued to operate as an export hub even after last week’s airstrikes. A satellite image showed three tankers at the island’s oil loading berths on Tuesday.

Analysts say that it is Iran’s closure of the strait, rather than control of Kharg Island, that is at the root of the country’s ability to exact a toll on global energy markets. The strait normally carries about a fifth of the world’s oil, and substantial amounts of natural gas. It is so narrow that Iran can harass ships there by launching small boats and firing weapons from its coast.

James M. Acton, the co-director of the nuclear policy program at the Carnegie Endowment for International Peace in Washington, said that control of the strait had emerged as such a powerful point of leverage that the regime was unlikely to fold even in the face of Mr. Trump’s threat to bomb Kharg Island’s oil terminal.

“Keeping the strait closed is of more value to them than the oil facilities on Kharg Island,” Mr. Acton said.

Mr. Trump said on Monday that it was not clear whether Iran had gone beyond firing at ships in the strait to mining its waters. U.S. officials said last week that Iran had started laying mines in the strait, The New York Times reported.

“We don’t know that any have even been dropped in,” Mr. Trump said. “If they do it, it’s a form of suicide.”

Mr. Trump appeared to be suggesting that by mining the strait, Iran would complicate its ability to export its own oil. But if Iran could no longer load its oil onto ships, the country would have less reason to allow a trickle of traffic.

“Seizing Iran’s most important oil hub would also fully eliminate any economic incentive Iran has to let any traffic go through the strait,” said Caitlin Talmadge, a professor at the Massachusetts Institute of Technology who has studied security issues in the Persian Gulf. “So it could backfire.”