The threat, he insisted, had to be “uprooted by an international front headed by the United States”.
Fast forward two decades. Mr Netanyahu, now Israel’s prime minister, is warning that the Islamic republic will be on the brink of developing the bomb by the middle of next year.
So how far is Iran from getting the bomb? Timeline estimates are fraught with uncertainty because it is not known how advanced the Iranians may be in their suspected nuclear bomb research.
Most experts believe it would take Iran at least two years to assemble a single nuclear-tipped missile, if it decided to do so.
Some, though, put it at just over half that time while US officials estimate Iran would need 12 to 18 months to build an atomic weapon.
Mr Netanyahu’s calculations are seemingly based on when Iran could have enough medium-enriched uranium to make a sprint to produce sufficient weapon-grade material for one bomb.
With provisos, many analysts agree with him that Iran could be in that position by next summer, although others say Tehran could need even less time.
But even if Iran makes a dash to enrich its uranium stockpile, it would probably need another six months to assemble a “crude nuclear device”, said Mark Fitzpatrick, a senior non-proliferation expert at the International Institute of Strategic Studies in London.
“And to produce a nuclear weapon that could be deliverable by a ballistic missile would take at least another year,” he added in an interview. “So the total time is at least two years.
“And that is only for one weapon. It would be foolhardy for Iran to undertake the risk, only to produce one nuclear weapon.”
Israel, the Middle East’s sole – if undeclared – nuclear-armed superpower is thought to have as many as 200 nuclear warheads.
Mr Fitzpatrick’s timeline, based on a review of open-source materials and discussions with government experts, tallies with a recent report signed by nearly three dozen high-ranking national security officials in the US.
They believe Iran would need between one and four months to produce enough weapons-grade uranium for a single nuclear device.
“Additional time – up to two years according to conservative estimates – would be required for Iran to build a nuclear warhead that would be reliably deliverable by a missile,” said the report, which was published by the Iran Project last month.
Among those endorsing the study – which was based on publicly available documents, – were two former US national security advisers, Zbigniew Brzezinski and Brent Scowcroft, and the former under secretary of state, Thomas Pickering.
Experts, moreover, say any attempt by Tehran to “break out” and make weapons-grade uranium would be spotted by the IAEA, which monitors Iran’s uranium stockpile.
Leon Panetta, the US defence secretary, said last month that Washington also has “pretty good intelligence” on Iran and would know if it decides to make a nuclear weapon. In that case, the US would have “a little more than a year” to act to stop it – and, he vowed, has the firepower to do so.