By Phil Stewart

MIAMI (Reuters) - The 10 U.S. sailors briefly held by Iran before being released on Wednesday made a navigational mistake that led them into Iranian waters but did not communicate that to Navy commanders before being intercepted, the U.S. military said on Thursday.

U.S. Defense Secretary Ash Carter said the information came from debriefings of the sailors, who were flown on Wednesday to a U.S. military facility in Qatar after Iran released them along with their two riverine boats.

"The information that they have given us, and through their commanders, is that they did stray accidentally into Iranian waters due to a navigation error," Carter said in an interview with FUSION television's Jorge Ramos, which will also air on Spanish-language Univision.

Carter's comments were the most detailed so far from American officials on the incident, which rattled nerves just before the expected implementation of a landmark nuclear deal between Iran and world powers.

Diplomats in Washington and Tehran, through a series of anxious phone calls, sought to resolve the incident quickly, ensuring it did not torpedo the nuclear accord.

In the end, Iran released the U.S. sailors - nine men and one woman - on Wednesday, a day after they were detained.

The speedy resolution of the incident contrasted with previous cases in which British servicemen were held considerably longer, in one case nearly two weeks.

Carter said the sailors apparently did not radio in to tell their commanders they were off-course before encountering the Iranians.

“They did not report this navigational error at the time. It may be that they were trying to sort it out at the time they encountered the Iranian boats and discovered they were inside of the territorial waters of Iran,” Carter said in the interview, that took place in Miami.

He denied the sailors were on a covert mission, saying that "they were simply transiting from one place to another."

Still, many questions about the incident remained unanswered, including what precisely led the sailors off-course and how they did not realize they were in danger before being detained by Iran.

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One U.S. official, speaking on condition of anonymity, said it was clear the boats did not run out of fuel.

IMAGES OF DETAINED SAILORS

Iranian state television has released footage of the arrest, showing the sailors as they knelt down with hands behind their heads and their two vessels being surrounded by several Iranian military fast boats.

It also released footage of one of the detained men, identified as a U.S. Navy commander, apologizing for the incident.

Carter acknowledged his discomfort over the images but urged against a rush to judgment.

"Obviously I don’t like to see our people being detained by a foreign military," Carter told a news conference later on Thursday at Tampa, Florida-based U.S. Central Command, which oversees American forces in the Middle East.

"I think we need to give these guys the opportunity to tell us what was really going on and what the overall context (was)."

General Lloyd Austin, who leads the U.S. military’s Central Command, said: "We’ll know a lot more after we’ve finished debriefing our sailors."

(Reporting by Phil Stewart; Additional reporting by Andrea Shalal; Writing by Susan Heavey and Phil Stewart; Editing by Dan Grebler and Peter Cooney)