Iran's Islamic Revolutionary Guard Corps (IRGC) said it had freed the sailors after determining they had entered Iranian territorial waters by mistake. The sailors had been detained aboard two U.S. Navy patrol boats in the Gulf on Tuesday.

"Our technical investigations showed the two U.S. Navy boats entered Iranian territorial waters inadvertently," the IRGC said in a statement carried by state television. "They were released in international waters after they apologized," it added.

Confirming the sailors' safe release, the Pentagon said there were no indications they were harmed while in Iranian custody.

A carefully worded statement did not explain how the sailors and their two riverine command boats ended up being detained by Iran, saying only that "the Navy will investigate the circumstances that led to the sailors' presence in Iran".

The sailors were later taken ashore by U.S. Navy aircraft, while other sailors took charge of the boats and headed towards Bahrain, their original destination.

U.S. Defense Secretary Ash Carter said he was pleased the sailors had been freed and appreciated "the timely way in which this situation was resolved".

He added: "I want to personally thank Secretary of State John Kerry for his diplomatic engagement with Iran to secure our sailors' swift return."