The US Federal Reserve has left interest rates on hold at 1% - the lowest level for 45 years - following its latest meeting.
It could be some time before Mr Greenspan alters rates
The Fed added that there remained a small risk that inflation could fall to an "undesirably low" level and so it expected to keep rates low for a "considerable period".
However, it noted that "spending is firming and the labour market appears to be stabilising".
The news was welcomed by US investors, with the Dow Jones closing up nearly 1.5% at 9,748.31 and the Nasdaq 2.6% higher at 1,932.26.
"It's bullish for the stock market, which takes support in easy monetary policy," said Rick Meckler, president at LibertyView Capital Management.
"Investors will think that the Fed wants to make sure that this recovery sticks and will take
a bullish view of the markets."
The low levels of interest rates and the tax cuts introduced by President George W. Bush appear to be helping economic growth.
Evidence is growing that the pace of recovery in the US economy is accelerating, with some economists estimating that growth hit an annualised rate of about 6% in the July to September period.
But analysts say the amount of slack in the US economy means the recovery does not pose any inflationary risks, and the Fed still appears concerned about the threat of deflation.
Last month, the core Consumer Price Index indicated prices were rising at an annual rate of just 1.2%.
"Despite all the euphoria among the economists with the regard to the latest set of data, the Fed still seems to be in the show-me camp," said David Rosenberg, chief economist for North America at Merrill Lynch.
"The bottom line is that there is still tremendous slack in the economy and inflation is inordinately low."
There was more good news for the US economy on Tuesday with the latest consumer confidence survey from the Conference Board showing sentiment picking up.
Figures from the US Commerce Department also showed a slight increase in orders for durable goods, and signs of a pick-up in business spending.