Saudi Arabia on Monday 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.
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.
Two other boats that also approached Marjan managed to escape after the Saudi navy fired warning shots, the agency reported.
The Saudi government is claiming that members on board the vessel approached its offshore oil field Marjan with the intent of carrying out a terrorist act, Reuters reports.
The Foreign Ministry spokesman said the Saudi coast guard's move to shoot and kill an Iranian fisherman was illegal and devoid of any justification.
"The individuals who came face to face with the Saudi forces are simple fishermen and their boat is a fishing boat", Aghababaei was quoted by Iran's Young Journalists Club as saying.
"This was one of three vessels which were intercepted by Saudi forces".
"The Kingdom of Saudi Arabia stresses its determination to combat and eradicate terrorism and its sources, as a part of the country's permanent objective to protect its national security against any external aggression", SPA said.
Riyadh, the UAE, Egypt and others severed diplomatic and economic ties with Qatar two weeks ago, accusing Doha of supporting groups, including some backed by Iran, "that aim to destabilise the region".
On Sunday Iran fired missiles into Syria, claiming it was hitting Islamic State targets in retaliation. "When Iran looks at ISIS it sees Saudi Arabia".