In a letter to U.N. Secretary-General Ban Ki-moon, Saudi authorities said Iranian helicopters flew several times over a gas field at Hasba, Abdullah al-Mualimi was quoted as saying in the daily newspaper Okaz on Monday.
The letter also said two Iranian navy boats intercepted a vessel belonging to state-owned oil giant Saudi Aramco.
"I have submitted to Secretary-General Ban Ki-moon a letter that details Iran's breaches of the official conventions and treaties between it and Saudi Arabia," Okaz quoted Mualimi as saying.
A Foreign Ministry spokesman declined to comment, saying the issue was under the jurisdiction of the Defence Ministry. A Defence Ministry spokesman was not available to comment.
Mualimi was quoted as saying the Saudi government had not requested international intervention but was "studying the appropriate practical steps to deal with the issue". He said the kingdom reserved the right to respond with appropriate action to protect its territory and oil.
The Saudi Foreign Ministry has sent a letter to the Iranian Foreign Ministry asking that such incidents are not repeated and stressing that the areas where the incidents occurred are Saudi-owned under agreements signed between the two countries in 1968, Mualimi said.
Separated by about 250 km (150 miles) of Gulf waters, Shi'ite Muslim power Iran and Sunni-led Saudi Arabia have often tense relations. Saudi Arabia has accused Iran of fomenting unrest among Shi'ites in its oil-rich Eastern Province, a charge Iran denies.
(Reporting by Asma Alsharif; Editing by Andrew Torchia and Janet Lawrence)