Dr Fox said Iran is the "biggest single emerging threat that we face" and must not be allowed to acquire nuclear weapons.
He attacked those who claim that renewing Trident, the British nuclear deterrent system, will be too expensive.
He compared the estimated £20 billion cost of renewal with the £12 billion cost of the London Olympics, saying: "You pay your money and you make your choices."
During a debate at Chatham House in central London with defence secretary Bob Ainsworth and Liberal Democrat defence spokesman Nick Harvey, Dr Fox said: "You are either going to allow Iran to become a nuclear weapons state or you are not going to allow Iran to become a nuclear weapons state.
"There are three reasons why we shouldn't allow it. Number one, the nature of the regime. In Iran you have an increasingly militarised state with a hard-line theocrat at the top.
"Number two, this is a state where par excellence they are willing to export terror and instability as part of their foreign policy. I would not like to see fissile material added to that particular mix. And thirdly, if Iran becomes a nuclear weapons state, Saudi Arabia, Turkey and Egypt will follow."
Dr Fox, who is opposed to unilateral disarmament for the UK, said the UK must not be left open to "nuclear blackmail" and said the "unavoidable consequence" of Iran gaining nuclear weapons would be a nuclear arms race in the Middle East.
He said more pressure must be applied on Tehran, adding: "It's inevitable that we are going to have to move to stronger sanctions and I think we should prepare for that. We should be preparing public opinion in Britain and in the rest of the European Union."
Mr Ainsworth agreed that Iran presents a strong threat. He said if Iran gained nuclear capability "we will wind up with a nuclear armed Middle East to a greater or lesser extent", and added: "We have to persuade Iran not to go down that path."
