He added that, in any case, even a sharp rise in rates would be unlikely to have much of a dampening effect on the value of technology shares.
Mr Greenspan was speaking at a White House summit on the new economy, where Microsoft's Bill Gates and dozens of Wall Street economists and entrepreneurs joined President Bill Clinton.
President Clinton said he wanted to focus attention on ways to harness the power and prosperity now evident in high-technology sectors of the US and world economy.
Mr Greenspan said the central bank, the Federal Reserve, was not trying to target share prices directly.
But he did issue a warning about the recent run-up in the price of technology shares.
"History will judge" whether the expectations of sharply higher profits for technology companies which have driven their share price rises was "prescience" or "wishful thinking".
The man with the power to move markets also said that there was little sign that the new economy-fuelled growth was likely to run out of steam soon.
Interest rate rises
"There can be little doubt that not only has productivity growth picked up from its rather tepid pace during the preceding quarter century but that the growth rate has continued to rise, with scant evidence that it is about to crest."
But he warned that sharp gains in equity prices risked fostering US inflation.
His remarks had little immediate effect on the stock market. The technology-heavy Nasdaq composite index rose more than 3% at one point before giving back most of the gains.
"Should changes in asset prices foster economic imbalances, as they appear to have done in recent years, it is the latter we need to address, not asset prices," he added.
The markets' recent ups and downs are widely expected to have little effect on the Fed's eagerness to continue raising interest rates, as it has done five times since last June in an effort to keep inflation at bay in the booming US economy.
Mr Greenspan also said that a more aggressive course of Fed tightening would be unlikely to make much difference to the run-up in share prices, which he has blamed for causing demand to outstrip supply and raising inflationary dangers.
"Even if we were to foster somewhat larger movements in short-term rates to address changes in stock prices, I doubt that investors' perceptions of equity risks would be much affected and thus that equity prices would be meaningfully influenced," he said.