Admiral Ali Fadavi said investigations had concluded "that this trespassing was not hostile or for spying purposes" and he was waiting to receive "the required order, which probably will be their release."
He said a broken navigation system had led the US sailors -- reportedly nine men and a woman -- to stray toward Iran's Farsi island.
The order for their release "won't take long," he was quoted as saying.
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"Naturally in territorial waters of the country any naval craft should announce their presence beforehand, especially if they are military," Fadavi added.
Iran's Foreign Minister Mohammad Javad Zarif was briefed about the incident.
Fadavi said Zarif had displayed "a strong stance" and had told US Secretary of State John Kerry that "these were our territorial waters and you should apologise," according to the state television report.
Two aircraft carriers -- the USS Harry S. Truman and France's Charles de Gaulle -- were both in international waters near Farsi island when the US boats were captured, the Guards said.