Rouhani also said Iran opposes any foreign forces in the region, the Middle East and the Persian Gulf, where the U.S. Navy's Fifth Fleet has a base in the tiny kingdom of Bahrain.
Earlier on Saturday, U.S. Defense Secretary Chuck Hagel laid out steps to beef up defense cooperation between states within the Gulf region, while at the same time insisting that America's military commitment to the Middle East will continue.
In a speech Saturday to Gulf leaders he also made it clear that the emerging global agreement that would limit Iran's nuclear program doesn't mean the security threat from the Islamic republic is over.
Iran's Defense Minister Gen. Hosein Dehghan called the remarks by his American counterpart "threatening," on Sunday, adding that they pave the ground for mistrust toward the U.S. while revealing the influence of Israel Iran's arch enemy on Washington.
Iran believes that countries of the Gulf are capable of managing security through regional security pacts.
Iran signed an interim agreement over its nuclear plan with world powers last month. Rouhani has been trying to convince skeptics and hard-liners at home that the move was not compromising on key issues of national sovereignty.
Israel has repeatedly criticized the deal and called it a "historic mistake", saying economic sanctions must be toughened, not eased.