Al-Hakim stressed that Israel's participation in such a mission was unacceptable, AP said.
"All of the Arab Gulf states are able to ensure the safe passage of ships in the Gulf", al-Hakim said.
On Thursday, Commander-in-Chief of the Revolutionary Guard Major General Hossein Salami warned that any new conflict in the region would be a major threat to Israel's existence, saying "a new war will put the Zionist regime under a full-scale threat".
The United States has been trying to persuade its allies to form an worldwide coalition with the declared aim of providing "security" for merchant shipping in the Strait of Hormuz - through which about a fifth of all oil consumed globally pass -and other strategic Middle Eastern shipping lanes.
Last week, Israel's Foreign Minister Yisrael Katz said that Israel would be providing intelligence and other assistance to "Operation Sentinel", a US-led effort to secure the Strait of Hormuz in the wake of multiple incidents in which Iranian naval forces seized foreign oil tankers in the vital shipping lane.
On August 9, Iranian Foreign Ministry Spokesman Abbas Moussavi highlighted that the Islamic Republic regards possible Israeli presence in a US-led coalition in the Persian Gulf as a clear threat to its national security, and reserves the right to counter it.
His comments came after Iran's defense minister said last week that the formation of a US-led flotilla would "increase insecurity" and any Israeli involvement would have "disastrous consequences" for the region. In July, Iranian commandos seized a British-flagged oil tanker, Stena Impero, in an apparent act of revenge after the United Kingdom seized an Iranian oil tanker near Gibraltar.