Sir John made the remarks at a meeting of around 100 senior civil servants in London last week in only his second public speech since he was appointed to the post in 2009.
Speaking at the Civil Service Live event in Olympia he said that Iran was now “two years away” from becoming a “nuclear weapons state”.
He said that “when that moment came” Israel or the United States would have to decide whether to launch a military strike.
“The Iranians are determinedly going down a path to master all aspects of nuclear weapons; all the technologies they need,” he said. “It’s equally clear that Israel and the United States would face huge dangers if Iran were to become a nuclear weapon state.”
Sir John said that without MI6’s work dealing with the threat, “you’d have Iran as a nuclear weapons state in 2008 rather than still being two years away in 2012.”
Sir John said it was up to MI6 to “delay that awful moment when the politicians may have to take a decision between accepting a nuclear-armed Iran or launching a military strike against Iran.”
When that moment came, he said: “I think it will be very tough for any prime minister of Israel or president of the United States to accept a nuclear-armed Iran.”
Iran has previously accused Israel and the US of trying to disrupt its nuclear programme through covert operations by Mossad, MI6 and the CIA.
Several Iranian nuclear scientists have been apparently assassinated in recent years while a powerful computer virus known as Stuxnet attacked the computer systems of their nuclear facilities.
Britain and America denied the allegations but Israel has remained silent on the issue.
Sir John disclosed that MI6 has “run a series of operations to ensure that the sanctions introduced internationally are implemented, and that we do everything we can within the Middle East to slow down these remaining problems.
“I take great pride in the fact that, in the last ten years, over a number of jobs, I’ve been involved in an issue of global concern, and I feel that I as an individual [have made] an impact in the outcome of events.”
The session – which was open to visitors to the event – was titled “Unclassified chat: Sir John Sawers CMG” and was reported in Civil Service World, a publication which is dedicated to senior Whitehall officials.
Disclosure of his remarks came as the US stepped up their sanctions against front companies suspected of supplying appaernt nuclear materials to Iran after an international oil embargo started earlier this month.
His warning of a nuclear Iran in 2014 could throw the Coalition into turmoil just before the next general election.
The Liberal Democrats have ruled out supporting any military action against the regime but David Cameron has repeatedly said that “all options” are on the table.
Senior Conservatives believe that the issue could finally cause the Coalition to split as Britain would be forced to support any American action.
In March, Sir John spoke to more than 20 ministers about the latest intelligence on the growing fear that Israel is poised to launch a pre-emptive strike against Tehran.
The secrecy around the briefing was so high that ministers were ordered to leave their mobile phones outside the Cabinet room.
There are claims that basic mobile phones, without specialist anti-eavesdropping security, can be converted into “listening devices” by foreign intelligence agencies.
The highly unusual briefing was thought to have raised questions about Israel’s military capacity to destroy Iranian nuclear sites, which are buried deep underground.
The MI6 chief was also understood to have warned about the potential threat to Britain from a nuclear arms race in the Middle East.
That came after Foreign secretary William Hague warned that Iran’s pursuit of nuclear weapons threatened to trigger a “new Cold War” that posed an even greater threat of nuclear conflict than the stand-off between the USSR and the West.
In an interview with The Daily Telegraph, Mr Hague said that Iran was threatening to spark a nuclear arms race in the Middle East which could be more dangerous than the original East-West Cold War as there are not the same “safety mechanisms” in place.
“It is a crisis coming down the tracks,” he said. “Because they are clearly continuing their nuclear weapons programme…
“If they obtain nuclear weapons capability, then I think other nations across the Middle East will want to develop nuclear weapons.
“And so, the most serious round of nuclear proliferation since nuclear weapons were invented would have begun with all the destabilizing effects in the Middle East.
“And the threat of a new cold war in the Middle East without necessarily all the safety mechanisms … That would be a disaster in world affairs.”