The Iranian Revolutionary Guards have released the ten detained U.S. sailors.
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Earlier, the Guards' top naval commander was quoted as saying that the sailors will "probably" be released.
"The final order will be issued soon and they will probably be released," IRGC Rear Admiral Ali Fadavi was quoted as saying by the Tasnim news agency, which is close to the Guards.
U.S. Secretary of State John Kerry expressed gratitude for the return of the American sailors and said in a statement, "That this issue was resolved peacefully and efficiently is a testament to the critical role diplomacy plays in keeping our country safe, secure and strong."
Iran said it detained the 10 sailors who were in two patrol boats in its territorial waters on Tuesday. Fadavi said the Guards' investigation showed a broken navigation system had led the sailors into Iranian waters.
The Guards also said that Tehran had asked the United States for an apology for "violating" Iran's waters.
"Iran's Foreign Minister Mohammad Javad Zarif was in touch with U.S. Secretary of State Kerry," Fadavi said in an interview broadcast live on state television.
"Zarif took a firm stance as the sailors had violated Iran's territorial waters and asked the United States for an apology," he added.
U.S. Vice President Joe Biden however, said that no apology was forthcoming.
"There's nothing to apologize for," said Biden in a CBS interview. "When you have a problem with the boat you apologize the boat had a problem? No, and there was no looking for any apology. This was just standard nautical practice."
Biden said that the Iranians realized the U.S. sailors "were there in distress and said they would release them and released them like ordinary nations would do."
The Pentagon said there are no indications that the sailors were harmed while in Iranian custody.
The carefully worded statement did not say how the sailors and their two riverine boats ended up being detained, saying only that "the Navy will investigate the circumstances that led to the sailors' presence in Iran."
On Tuesday, two U.S. officials told Reuters that it was unlikely the sailors would be released overnight, and a defense official said that plans were in place to return them to the U.S. Navy early Wednesday morning.
Earlier, U.S. defense officials said the sailors - nine men and one woman - had been on two riverine patrol boats when they were taken into Iranian custody. The United States says the ships were en route from Kuwait to Bahrain at the time.
Tuesday's event was the latest reported incident between U.S. and Iranian forces in the Gulf in recent weeks. The U.S. Navy said late last month that an Iranian Revolutionary Guards vessel fired unguided rockets on December 26 near warships including the aircraft carrier USS Harry S. Truman in the Strait of Hormuz. Iran denied the vessel had done so.