US Secretary of State John Kerry has thanked Iran for ending what could have been a crisis involving the Islamic Republic holding 10 US sailors, who have now been freed.

Kerry said in a statement on Wednesday: "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."

Kerry has a close relationship with Iranian Foreign Minister Mohammed Javad Zarif after the recent nuclear deal between the Islamic Republic and world powers.

The nine American men and one woman were held in an Iranian base on Farsi Island in the Persian Gulf after being detained nearby on Tuesday. The US military has said that mechanical trouble with one of the boats caused them to drift into Iranian territorial waters near the island, where they were picked up by Iran.