The U.S. commander who spoke on camera has indicated he felt pressure to talk about how well they were being treated. It's not yet clear if he was directly ordered to apologize, the official said.
The U.S sailor was filmed saying, "It was a mistake that was our fault and we apologize for our mistake."
While the nine men and one woman sailor were not physically mistreated, the information from the defense official was the first indication they were under some direct mental duress from the Iranians.
The Iranian state-run TV footage of the sailors being captured, on their knees with their hands behind their heads, and a subsequent video of one sailor apologizing has been fodder for Republican critics of President Barack Obama since the news first hit just hours before his final State of the Union. The latest details could further fan the flames.
As more information has come to light through the debriefs, it's now understood that the crew decided to "cut a corner" to make up time to get to a planned refueling point. It's not clear whether they were lower on fuel than expected.
That change of course began a series of events that led them apparently unknowingly into Iranian waters, officials said.
The crew stopped to fix an engine problem on one of the boats, not realizing they had drifted too close to Iran's Farsi Island, the official said.
Two others defense officials also said it appears the crew was so involved in fixing the engine that they didn't realize where they were until the Iranians boats approached them.
All three officials strongly emphasized the full investigation must be completed before the military will be certain about what happened.
The footage of the sailors was a hot topic in the Republican debate Thursday night -- Donald Trump closed the event by saying: "I stood yesterday with 75 construction workers. They're tough, they're strong, they're great people. Half of them had tears pouring down their face. They were watching the humiliation of our young 10 sailors, sitting on the floor with their knees in a begging position, their hands up."
But the Obama administration, including Secretary of State John Kerry and Defense Secretary Ash Carter, has held fast to the argument that establishing an open line of communication with Iran over the past few years was directly responsible for the safe and quick return of the sailors Wednesday.
White House spokesman Josh Earnest said Friday that if the administration had followed the advice of its critics, the U.S. would probably be at war with Iran.
The incident "underscores the value of responsible, mature leadership," Earnest said. "The President didn't start a war over this."