In testimony on monetary policy before the House Financial Services Committee, Mr Greenspan said the American economy still faced considerable uncertainties, and interest rates may need to be lowered further.
"Pressures on profit margins have been unrelenting... weakness is evident virtually across the board," he said.
But all-out panic in the markets was averted, after a series of respectable corporate results and indications that US consumer spending remains relatively robust.
By the close on Wednesday evening, most of the worst losses had been at least partially reversed.
The tech-heavy Nasdaq finished with a loss of 2.5%, after diving more than 3% at mid-afternoon, while the blue-chip Dow Jones industrial average fell 36.56 points, or 0.34%, marking a substantial recovery from its earlier loss of 122 points.
Signs of hope
In an optimistic note in what was otherwise a gloomy speech, Mr Greenspan pointed out that consumer demand - a key element in America's prolonged economic boom in the 1990s - remained strong.
And during questioning after his speech, he sounded an even more optimistic note, indicating that the slump may already have bottomed out.
But "we are not free of the risk that economic weakness will be greater than currently anticipated, and require further policy response," Mr Greenspan warned.
Inflation has been a key worry.
US consumer prices rose by 0.2% in June, or by 0.3% if food and energy are excluded - well above expectations, and more than the 0.1% increase recorded in May.
Higher inflation makes it less likely that the US Federal Reserve would cut interest rates at its next meeting in late August.
But analysts were divided on whether the inflation figure really was gloomy, or a welcome sign that underlying US demand remained strong.
"It just doesn't make a whole lot of sense that we're going to have an inflation problem in the midst of a period where economic growth has slowed very dramatically," said Anthony Karydakis, senior financial economist at Banc One Capital Markets.
Mixed results
The optimistic scenario was given further support by a series of strong second-quarter results from some of the country's biggest companies.
The strongest performances were from consumer-oriented companies.
AOL Time Warner, the world's biggest media firm, reported a 20% surge in profits for the quarter, while food and beverage companies Coca-Cola and Kraft saw double-digit earnings growth.
And in a rare sign of hope for the troubled high-tech sector, IBM announced a modest increase in second-quarter profits.
The cheer was diminished, however, by the news that Sears, the country's biggest non-food retailer, saw second-quarter profits fall by 13%.
Car maker Ford and camera company Polaroid, both of which have been suffering legal and financial difficulties, dropped into loss for the quarter.
So did American Airlines, the world's biggest carrier, as the effects of a market slowdown and high fuel costs started to bite.
And financial firms have performed poorly, along with the slump in markets.
JP Morgan, the number-two US bank holding company, said earnings before charges fell 61% in the quarter.