Donald Trump has kept the world guessing with his war in Iran, rushing thousands of troops to the region in a show of force while boasting of progress in talks that Tehran denies are happening.

The US says it has destroyed more than 10,000 targets and over 100 Iranian ships since its war began in February, but the Strait of Hormuz remains under Iran’s grip, causing a crisis in global markets and weakening US leverage.

A large island housing anti-ship missiles in the Strait has been briefed as a possible target of a ground offensive to break Iran’s grip, alongside key oil export hub Kharg Island.

Qeshm is a 558sq mile stretch off mainland Iran that has been fortified with an underground missile “city” that is used intermittently to attack ships passing through the waterway.

In peacetime, Qeshm is a tourist destination dotted with salt caves and the remnants of fortifications installed by European empires. The Royal Indian Navy operated out of the island until 1863 and the last coaling station for the Royal Navy was abandoned in 1935 at the request of the Shah.

Since then, Iran has reconstituted the island with missiles, drones and fast-attack boats. Exact details are kept confidential, but retired Lebanese Brigadier-General Hassan Jouni, a military and strategic expert, told Al Jazeera that the island has the ability to strike from an underground “missile city”.

According to Can Kasapoğlu, a defence analyst, satellite imagery suggests Iran has installed a “significant portion of its anti-ship missiles in underground launch positions on Qeshm”.

He wrote for the Hudson Institute, a conservative think tank based in Washington, that “any US campaign in the region would likely centre on two decisive islands: Kharg and Qeshm”.

Kharg island handles some 90 per cent of Iran’s oil exports, and taking it would give the US the ability to disrupt Iran’s energy trade and place enormous pressure on the economy. Iran has fortified the island with additional surface-to-air missiles and laid traps including anti-personnel and anti-armour mines in the waters surrounding it, CNN reported, citing people familiar with US intelligence.

Qeshm, meanwhile, operates as the Islamic Revolutionary Guard Corps’ (IRGC) “primary denial hub”, a much larger base designed to shut the door on traffic approaching the Strait of Hormuz, Mr Kasapoğlu explained.

“Taking Qeshm is also most likely the harder fight,” he wrote. “The island’s size, terrain, and proximity to the mainland favour the defender. Iranian reinforcement efforts there would likely be continuous.”

Even if the US can take it, it would come at a high cost with relatively little strategic return, he said.

Rashid Al-Mohanadi, vice-president of Centre of International Policy Research and an expert in Gulf security told The Telegraph that “Qeshm is likely to have the whole shebang” prepared for a possible invasion.

“Of course the island would have anti-ship capabilities, the coast is likely mined, the beaches booby-trapped and so on,” he said, adding that an additional threat would come from Iran’s ability to launch strikes from the mainland.

While Trump has said the US and Iran are making progress in talks, he has also been sending more ​troops to the region, leading Iran’s parliament speaker to accuse Washington of sending contradictory messages about negotiations while planning a ground invasion.

The Wall Street Journal reported late on Tuesday that the UAE is now preparing to help the US and allies open the Strait by force, having suggested the US occupy strategic islands, according to the report.

But in shifting remarks, the president also said on Tuesday that the US could leave within as little as two weeks and without having to agree a deal with Tehran.

Asked if successful diplomacy was a prerequisite for the US to end what it calls “Operation Epic Fury”, he told reporters: “Iran doesn’t have to make a deal, no.”