The seizure risks becoming a major international spat, at a time when Iran is in delicate negotiations with Western powers for sanctions to be dropped in exchange for a halt to its nuclear enrichment program.
The Pentagon saying it is monitoring the seizure situation and U.S. officials have branded the Iranian action as "inappropriate," according to various media reports.
The Strait of Hormuz is in Iranian territorial waters, within 12 miles of the Iranian coast, but is recognized as containing international shipping lanes, according to the Pentagon. This means that the principle of "innocent passage" should be applied, meaning that law-abiding foreign ships should be allowed to pass, the Pentagon said.
Danish-owned Maersk Line said it had contacted Iranian authorities and been told that the seizure was "related to an allegedly unresolved cargo claim."
"We have however not received any written notification or similar pertaining to the claim or the seizure of the vessel," said Maersk Line's Storgaard in a news statement on Wednesday.
"We are therefore not able to confirm whether or not this is the actual reason behind the seizure. We will continue our efforts to obtain more information."
However, Iran's Fars news agency reported that "the vessel had been seized for trespassing on Iran's territorial waters in the Persian Gulf."
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One maritime expert following the situation, who preferred not to be named, said the seizure was a diplomatic rather than shipping issue.
"It's not a legitimate argument that the Iranians are using to say that arresting a vessel at sea is normal procedure. If a vessel is arrested it would usually always happen in a port, rather than at sea," the expert told CNBC on Wednesday.
The expert said that while a lot of detail had yet to emerge about the seizure, he found it "hard to believe" that it was due to a "civil matter," as Iranian officials were reported to have said on Tuesday.
"It's certainly not normal practice to go around arresting vessels like that," the expert added.
The shipping lane where the Maersk Tigris was stopped is one the busiest shipping lanes in the world, making Iran's actions more surprising, given that disruptions to cargo containers could have an impact on global trade and diplomatic relations.
Albert Stein, managing director of AlixPartners, which compiles an annual shipping industry outlook report, told CNBC on Wednesday that Iran's action was a one-off—but the country could be playing with fire.
"This is one ship and it looks like a one-off, but if this is repeated then there will be a much bigger problem for everyone. But from a shipping industry perspective, we certainly haven't seen much movement in the insurance rates for the Straits of Hormuz."
He forecast the ship would be released fairly soon and said that most ship owners would not be put off using the Straits of Hormuz, given that the passage was a key trading route. "Frankly, they don't have much of a choice," he said, with the Middle East reliant on that lane for its goods.
Around 90 percent of the world's goods are still transported by ship, according to the International Maritime Organization.
The shipping industry certainly does not need any more turbulence at the moment. The Baltic Dry Index, which measures the cost of transporting major materials by sea and is seen as a key indicator of global demand, is hovering around 600, far below the 1,484 level of last November.
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