Iran’s president has warned American and other foreign forces to “stay away” from the region, as Tehran paraded long-range missile capable of reaching American bases.

Hassan Rouhani said the presence of such troops in the Gulf has always brought “pain and misery”, in a speech made at an annual military parade to commemorate the war with Iraq.

Mr Rouhani spoke in response to an announcement made by the US on Friday that it was sending more troops to Saudi Arabia after an attack on Saudi oil facilities both nations blame on Iran.

Iranian Turkmen Basij militia members marching during the annual

"Wherever the Americans or our enemies have gone, there has been insecurity afterward,” the Iranian president said. “The farther you keep yourselves from our region and our nations, the more security there will be."

At the parade, the Islamic republic displayed the Khordad-3 air defence system that shot down a US drone in June. It also showcased the long-range, surface-to-air Bavar 373 missile that can travel more than 1,250 miles, bringing it in range of US bases in the region and arch-foe Israel.

Iranian President Hassan Rouhani is seen during the ceremony of the National Army Day parade in Tehran Credit: Wana News Agency

Saudi Arabia and the US accuse Iran of attacking Saudi oil facilities on September 14, the biggest such assault on the world’s top oil exporter.

Iran denies involvement in the attack, which was claimed by Yemen’s Houthi movement, a group aligned with Iran and currently fighting a Saudi-led alliance in the civil war.

US President Donald Trump had said it would step up to protect Saudi but would take its cue from Saudi.

Riyadh has said it has evidence Iranian missiles were used in last weekend’s attack and that they were launched from the north, but did not go so far as to say they came from Iranian territory.

Iranian President Hassan Rouhani delivers a speech during the ceremony of the National Army Day parade in Tehran Credit: Wana News Agency

Should the accusation be proven, it would mark such a serious escalation in the long-running conflict between Saudi and Iran that the former could be forced to retaliate.

"We hold Iran responsible because the missiles and the drones that were fired at Saudi Arabia were Iranian-built and Iranian-delivered," Adel al-Jubeir, Saudi’s Minister of State for Foreign Affairs, said on Sunday.

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"But to launch an attack from your territory, if that is the case, puts us in a different category... this would be considered an act of war," he told CNN.

Both sides are holding their nerve, hoping to make their case to the United Nations General Assembly later this week.

Mr Rouhani, along with US sanctioned Foreign Minister Mohammad Javad Zarif, will travel to New York on Monday, to present what he called a security plan for the Gulf.

President Hassan Rouhani, left, listens to chief of the Revolutionary Guard Gen. Hossein Salami at a military parade marking 39th anniversary of outset of Iran-Iraq war Credit: Office of Iranian Presidency

"In this sensitive and important historical moment, we announce to our neighbours that we extend the hand of friendship and brotherhood to them," he said.

It is unclear what this would look like, with the president saying only that peace in the Strait of Hormuz could be achieved "in co-operation with various countries."

The US has already formed its own maritime coalition in the Gulf to secure one of the world’s most vital oil trade routes with the UK, Saudi, Bahrain and even the UAE, which has tried to keep good relations with Tehran since the most recent tensions began.

Members of Iran's Islamic Revolutionary Guard Corps (IRGC) standing in formation during the annual "Sacred Defence Week" Credit: AFP

British former diplomats said Iran, which has been hit by wave after wave of US sanctions after Mr Trump pulled the country out of the landmark nuclear deal last year, is counting on the US and Saudi not wanting to start war.

“I think it is a matter of the hardliners in Iran looking to shore up their influence by keeping tensions with the US high, while still maintaining just enough deniability to preempt a full US response,” Charles Hollis, a British former diplomat in both Riyadh and Tehran, told the Telegraph. “Assisted by a growing belief that Trump may talk tough but is not willing to act.”

In the US, Mike Pompeo, the American Secretary of State, squarely laid the blame for the attacks on the Saudi oil fields on Iran.

“No reasonable person doubts precisely who conducted these strikes, and it is the Intelligence Community’s determination that it is likely the case that these were launched from Iran,” he said on Face the Nation.

“This was a sophisticated attack. These weapons systems had ranges that could not have come from the Houthis. It is crazy for anyone to assert that they did.

Mike Pompeo dismisses Iranian denial of responsibility for oil field attacks Credit: Susan Walsh/AP

“I mean, it is literally nuts on its face to make an assertion that this was an attack by the Houthis. This was Iran true and true, and the United States will respond in a way that reflects that act of war by this Iranian revolutionary regime.”

Mr Pompeo dismissed the denial of responsibility by Iranian Foreign Minister Mohammad Javad Zarif.

“I don’t know why anybody listens to the Iranian foreign minister. He has nothing to do with Iranian foreign policy and he has lied for decades, and then he resigned.

“It’s just – it’s not even worth – it’s not even worth responding to him. It’s beneath the dignity of anyone in the world to listen to someone who repeatedly makes the claim that the Houthis launched this attack.”

Speaking on the same programme, Mr Zarif was pessimistic that conflict with the US could be prevented.

"No, I'm not confident that we can avoid a war," Zarif said on "Face the Nation" Sunday. "I'm confident that we will not start one but I'm confident that whoever starts one will not be the one who finishes it."