Story highlights Secretary of State John Kerry spoke to his Iranian counterpart, Iranian Foreign Minister Javad Zarif, at least five times Tuesday

The State Department maintains Kerry never offered an apology to Iran over the incident

Washington (CNN) Secretary of State John Kerry spoke to his Iranian counterpart, Iranian Foreign Minister Javad Zarif, at least five times Tuesday while U.S. Navy sailors were in Iranian custody, a senior State Department official told reporters Wednesday.

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.

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