WASHINGTON: US Secretary of State John Kerry said Monday he was “frustrated and angry” at an Iranian video showing 10 detained US Navy sailors, as the American military described how the nine men and one woman were surrounded by machine gun-toting Iranian personnel.

His comments come a day after the two countries hailed the implementation of Tehran's nuclear deal, with President Barack Obama saying the breakthrough was vindication of his contentious policy of engagement with Iran.

However, underlining the lingering deep suspicions between the two sides, Iran seized 10 sailors last week in the Gulf after their boats strayed into Iranian waters and held them overnight.

Read more: Iran frees 10 US sailors as diplomacy smoothes waters

They were freed on Wednesday after Iran accepted they entered by mistake.

Video footage showed the US Navy personnel kneeling with their hands behind their heads as they were apprehended, something Kerry made clear he was deeply unhappy about.

“I was very angry. I was very frustrated and angry that that was released,” Kerry told CNN, saying the footage was released by the Iranian military or Revolutionary Guards, not the government.

“But I am not excusing it, there was no excuse for it. Our sailors regretably, and inadvertently, went into Iranian waters.”

The strongly worded remarks came as the US military released its first detailed account of the incident, which threatened to spark a renewed crisis between Tehran and Washington.

One of the two US riverine patrol boats (RCBs) “had indications of a mechanical issue in a diesel engine,” said a statement from US Central Command (Centcom), and both vessels stopped.

“This stop occurred in Iranian territorial waters, although it's not clear the crew was aware of their exact location. While the RCBs were stopped and the crew was attempting to evaluate the mechanical issue, Iranian boats approached the vessels.”

Centcom said that there were soon four Iranian vessels at the scene, all with armed personnel aboard and after a conversation between the two sides armed Iranian military boarded the RCBs.

Meanwhile, Iranian personnel on their own vessels kept watch with mounted machine guns and the US boats were then escorted at gunpoint to Farsi Island.

“A post-recovery inventory of the boats found that all weapons, ammunition and communication gear are accounted for minus two SIM cards that appear to have been removed from two handheld satellite phones,” said the US Central Command, which oversees US operations in the Middle East.

Earlier, US Defence Secretary Ash Carter said he was pleased the sailors had been freed and appreciated “the timely way in which this situation was resolved”.

Carter had personally thanked Kerry for his "diplomatic engagement" with Iran to secure the sailors.

'No link between Iran freeing Americans and sanctions lifting'

John Kerry said Monday there was no direct link between the release of Americans detained in Iran and the lifting of punishing sanctions against Tehran.

In two days of fast-moving diplomacy at the weekend, five Americans were freed by Iran on Saturday and on Sunday the US and Iranian presidents hailed the implementation of Tehran's nuclear deal, which saw Washington and the European Union lift sanctions.

Kerry told CNN that the timing was coincidental and that the Americans would have been released even if the sanctions had remained in place.

“It happened to come together at that moment, I think that everybody saw that that would be propitious, but it was not directly linked,” he said.

“I had hoped it (their release) would have happened a couple months ago actually and then it hit a snag and we continued to negotiate.”

Read more: Nuclear sanctions lifted as Iran and US agree on dramatic prisoner swap

Four of the American prisoners, including Washington Post journalist Jason Rezaian, were freed in exchange for Washington pardoning seven Iranians accused of sanctions-busting.

A fifth American was also released in a separate process.

Kerry also confirmed a report by The Washington Post that the flight out of Iran of Rezaian and two of the other Americans was delayed because of a mix-up over the fate of Rezaian's wife Yeganeh.

“It did hit a snag because word somehow had not been communicated with the respect to the manifest on the plane that Jason Rezaian's wife would be coming with him,” Kerry said.

However, the Iranian government quickly understood that “the terms of the agreement included her,” said Kerry.

“We went through a period of time while they were located and ultimately reunited with Jason, and now all is well that ends well.”