Majid Aghababaie, head of border affairs at Iran's interior ministry, said the three people detained were fishermen from the southern Iranian port of Bushehr.
"The identity of those three individuals is known. They are from Bushehr and were fishing when they were arrested by the Saudi coastguard," said Aghababaie.
"There is no proof that they are military personnel," he said, in remarks carried by the ILNA news agency.
Saudi Arabia today said the three suspects it captured were Guard members aboard a boat heading to an oil platform in the Gulf, which separates the two rival nations.
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"It is clear this was intended to be a terrorist act in Saudi territorial waters designed to cause severe damage to people and property," the ministry said.
On Saturday, Iran accused the Saudi coastguard of killing one of its fishermen after two fishing boats may have strayed into Saudi waters.
Aghababie said today that a Saudi claim the boats entered the kingdom's waters had not been proven.
"But the day of the incident (Saturday) one of the two boats had a mechanical failure and the Saudi forces opened fire killing a fisherman," he said.
It said the incident took place on Friday night.
One boat was captured, while the other two escaped, a Saudi government statement said.
Tensions between Sunni-led Saudi Arabia and Shiite- dominated Iran are chronic.
Saudi Arabia regularly accuses Iran of interfering in the affairs of its neighbours, claims rejected by Tehran.