Greenspan, presenting the Federal Reserve Monetary Policy Report, said he had room to cut interest rates further.
His comments came just three weeks after the Federal Open Market Committee (FOMC) trimmed the key federal funds target rate by a quarter point to a 1958 low of 1.00 percent.
The Federal Reserve would keep rates low for "as long is takes" to spark a satisfactory recovery, he said.
Greenspan slashed the 2003 economic growth forecast by 0.75 percentage points to 2.50-2.75 percent, when comparing the fourth quarter of 2003 to the fourth quarter of 2002. Growth was expected to rise to 3.75-4.75 percent in 2004.
Months after the Iraq war, the economy now remained hemmed in by cautious businesses refusing to invest or hire more workers, the powerful 77-year-old central bank chief said.
The US jobless rate hit a nine-year high of 6.4 percent in June as businesses axed 30,000 jobs.
"Continued global uncertainties and economic weakness abroad, particularly among some of our major trading partners, also have extended the ongoing softness in the demand for US goods and services," he added.
Many of the economic uncertainties of the Iraq war had been resolved, however, stocks and bonds had strengthened, and low interest rates had boosted business profits and enriched people by driving down mortgage rates, Greenspan said.
Deflation had become a real, if remote threat, Greenspan said. "There is an especially pernicious, albeit remote, scenario in which inflation turns negative against a backdrop of weak aggregate demand, engendering a corrosive deflationary spiral," he said.
Meanwhile, the White House on Tuesday called a reported 450-billion-dollar shortfall for this fiscal year "manageable" and predicted that it would halve the US federal budget deficit "over the next few years."
The Bush Administration was responding to reports that the US budget deficit could soar above 450 billion dollars this year, some 50 percent higher than it estimated earlier this year.
If the figure of 450 is reached, it would far exceed the previous record deficit of 290 billion dollars reached in 1992, the reports said.