In the course of his conversations, the official said Kerry told Zarif: "If we are able to do this the right way, we can make this into what will be a good story for both of us" and would be a way for Iran to prove it can act in a responsible manner in this type of situation.
The calls, which took place over a period of at least 10 hours, began at 1:00 p.m. ET after Kerry had a chance to discuss the American understanding of the situation with Joint Chiefs Chairman Gen. Joseph Dunford and National Security Adviser Susan Rice.
While the initial call with Zarif had already been planned in advance, the official said it "took on a different degree of importance" because of the situation with the sailors.
Kerry, who was already hosting Defense Secretary Ashton Carter and their two Filipino counterparts at the State Department, excused himself from those meetings to begin the telephone diplomacy after he became aware of the incident.
In his first call with Zarif, the official said Kerry explained the U.S. understanding of what had transpired: that the sailors were in transit from Kuwait to Bahrain and may have encountered mechanical problems, and the United States had lost contact with them. Kerry "made it clear" that the most important thing was for the sailors to be released immediately and unharmed, the official said.
After a series of follow-up conversations with Carter, Dunford and Rice, Kerry spoke to Zarif again at 2:00 p.m., followed by another call around 3:15 p.m. It was during that second call that Zarif told Kerry he was getting indications from those holding the sailors that they would be released at some point after dawn, and were being fed and well treated.
Kerry relayed this information to the White House and the Pentagon, according to the official.
While there were a series of additional short conversations between Kerry and Zarif throughout the day to exchange information, there was a final call at approximately 10:30 p.m. following President Barack Obama's State of the Union address, when Kerry was assured everything was still on track for the sailors' release.
The official credited the relatively quick resolution of the situation to the relationship built up between the two countries over the course of the negotiations of the nuclear deal with Iran and said the situation "undoubtedly would have been more complicated to unwind," in the absence of that framework.
And while video surfaced on Iranian television purportedly showing one of the U.S. sailors apologizing for the incident, the State Department maintains Kerry never offered an apology to Zarif on behalf of the U.S. government, and merely offered explanations for how the situation unfolded.
"I don't think there's necessarily a need for any kind of apology," State Department Deputy spokesman Mark Toner told reporters Wednesday.
State Department officials also say the incident involving the sailors will not have an impact on the final implementation of the nuclear deal, which Iranian officials have indicated will be coming soon.
"The fact that we were able to de-escalate, we were able to resolve the situation diplomatically, again, speaks to the fact that we have this dialogue now with the Iranians," Toner said.