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."
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."