WASHINGTON — Four hours behind schedule and 300 miles from their destination in Bahrain, the crews of two Navy patrol boats figured they had to make up time somehow. Immediately after leaving port in Kuwait, they veered off their planned route through the Persian Gulf, and their troubles began.

First they accidentally sailed through Saudi Arabia’s territorial waters. Then one of the boats broke down while passing less than two miles from an Iranian-controlled island. When Iranian military boats swarmed the American vessels, they tried to get away. But the Iranians blocked their path and took the crews captive.

Navy officials on Thursday gave that account of the encounter in January that resulted in the detention of 10 American naval personnel for about 15 hours by the Iran’s Revolutionary Guards. In a stinging report, the officials described numerous mistakes in the way the mission was planned and executed, and they laid out the reasons some sailors were responsible, both on the boats and up the chain of command.

Nine officers and enlisted sailors — including a captain and the commanding officer of the boats — face discipline, with some being relieved of command because of the episode, which embarrassed the service and occurred just hours before President Obama gave his last State of Union address.