Within minutes of his remarks, delivered in his regular twice-yearly report on the economy to the Senate Banking Committee, the Dow had plunged more than 100 points, while the 30-year Treasury bond fell more than a point.
Both markets recouped part of the losses later, with the Dow ending the day below the 7,000 level at 6,983.18, a fall of more nearly 55 points.
In London, the FTSE 100 index ended more than 15 points down at 4,329.3. This was up from its low and only 33 points below its record.
As ever, Mr Greenspan's utterances were dry and Delphic, as he listed the reasons the US economy had lately performed so well, combining solid growth with low inflation: "Even I must admit that our economic prospects in general are quite favourable."
Among the reasons he gave were a strong dollar which braked imported inflation, a lingering job-market insecurity that had tempered wage demands, and big profit margins that allowed companies to absorb higher costs without raising prices.
But he added in the next breath, that while the central bank still expected US inflation to stay below 3 per cent in 1997, these special factors could well prove temporary. And, he hinted, given the time required for interest rate changes to work through into the economy, what would be the Fed's first raise in short-term rates since 1 February 1995 could be just around the corner.
"A pre-emptive policy tightening," he said, "may become appropriate before any sign of actual higher inflation becomes evident."
Mr Greenspan seemed most concerned, however, by the rampant stock market, which last week breached the 7,000 barrier, a rise of some 10 per cent since he famously proclaimed last December his fears over "irrational exuberance" in the equity market.
Yesterday, he seemed to be making another attempt to talk prices down without using the big stick of higher interest rates. Caution, he declared, seemed "especially warranted" over the sustained advance in prices. Referring explicitly to his previous warning which markets brushed aside in barely 24 hours, he re-iterated that "there are reasons in the current environment to keep this question on the table".
More specifically, he cast doubt on the fashionable belief that fundamental changes in economic conditions - global competition and new information technology are the two most often cited - justified the surge in stock prices.
There might be reasons to believe in something "fundamentally new." But, he went on, "history is strewn with visions of such `new eras' that in the end have proven to be mirages. In short, history counsels caution. Such caution may be especially warranted with regard to the sharp rise in equity prices during the past two years".
On balance, Mr Greenspan's words have strengthened the chances the Fed's interest rate steering committee will opt for a small increase in the Fed funds rate - currently at 5.25 per cent - when it next meets on 25 March. If not then, most analysts expect a move before June.
Even so, the central bank reckons the current steady expansion will continue.
Its 1997 forecast predicts growth of between 2 and 2.25 per cent, and an unemployment rate of 5.5 per cent or less for the rest of the year.
In the UK gilts were hit more than shares by Mr Greenspan's warning. But a pounds 2.5bn auction of gilts by the Bank of England earlier in the day was a moderate success, subscribed just under two times.