In his first comments on the matter, Rouhani said: "We have a clear response to these efforts; the Israelis had better ensure the security of where they are". The Navy also said the unit includes military personnel with a lot of experience in overseas missions.
He went on to say that Iran is seeking cooperation with its neighbors and is pursuing joint interests with the countries of the region.
"We are reviewing various ways to protect our ships (in the Strait of Hormuz)".
Islamic Revolutionary Guard Corps naval commander Alireza Tangsiri warned Sunday that "any illegitimate presence by the Zionists in the waters of the Persian Gulf could spark a war", after Israel announced that it was taking part in a US-led mission to secure the Strait of Hormuz.
The United States wants an global coalition to monitor and potentially escort commercial ships there.
But the officer said no formal decision has been made for the unit to join the US-led campaign.
In this photo released by the official website of the office of the Iranian Presidency, President Hassan Rouhani attends a meeting with Foreign Minister Mohammad Javad Zarif and the country's senior diplomats in Tehran, Iran, Tuesday, Aug. 6, 2019.
The US have since bulked up their naval presence in the Gulf, deploying additional forces inclining air craft carriers and B-52 bombers. Israel's contribution to the mission would be limited to intelligence.
Al-Hakim stressed Israel's participation in such a mission was unacceptable.
In June, Iran shot down an American surveillance drone in the Strait of Hormuz, and the U.S. came close to responding with military firepower.
Iran has threatened to disrupt oil shipments through the waterway, where several oil tankers have been attacked, if the United States tries to strangle its economy with sanctions on its vital oil exports.
In remarks in 2016, Leader of the Islamic Revolution Ayatollah Seyed Ali Khamenei underlined that security of the Persian Gulf region comes within the purview of the regional countries alone, and dismissed the United States claim of seeking security in the region.
Oil tanker traffic passing through the Gulf via the Strait of Hormuz is the focus of a US-Iranian standoff since Washington pulled out of an worldwide nuclear deal with Iran.