"I suspect the American economy is in an upswing - it's not going to be a dramatic upswing ... but events look increasingly positive," Greenspan said in response to questions during a panel discussion at the annual International Monetary Conference with other central bankers.
The U.S. economy, which was hit by its first recession in a decade last year, rebounded at an annual rate of 5.6 percent in this year's first quarter. But Greenspan said that in the future, "We will not grow at the pace of the first quarter."
This tallies with the views of many private forecasters who say the economy will have lower growth rates of between 3 percent and 4 percent for the rest of the year. U.S. unemployment, currently at an eight-year high of 6 percent, is expected to peak around 6.5 percent later this summer before starting to decline.
The central bank, after pushing interest rates to a 40-year low of 1.75 percent last year to fight the recession and the shocks from the September 11 terrorist attacks, has left rates unchanged so far this year.
Many analysts believe interest rates will remain on hold until at least the FOMC's August meeting, waiting for signs that the jobless rate has begun to fall.
The central bank has room to maneuver, because so far inflation outside of energy prices has remained moderate. In his remarks on Tuesday, Greenspan said businesses still had very little power to raise prices because of the lingering effects from last year's recession. But he cautioned that it would be a mistake for central bankers to let down their guard against the threat of inflation.
Greenspan said last year's recession, the first in the United States since 1990-91, would turn out to be the shallowest of the past 50 years. For that reason, he said the rebound this year would be "pedestrian", because the economy did not have to make up much lost ground.
He said the U.S. economy was able to bounce back so quickly from the recession and the terrorist attacks because of a "dramatic increase" in the use of information technology by companies, which allowed them to adjust quickly to changing circumstances.
He also credited the growing use of derivatives, financial instruments that are linked to the underlying value of a certain asset such as stocks or commodities. He said companies used derivatives to spread their risks.
These factors had allowed for a quick rebound from events such as the terrorist attacks that "would have upended the economy" in the past, Greenspan said.
His comments came at the International Monetary Conference, an annual event in which top officials at the world's largest banks meet with central bankers to discuss problems facing the international financial system.
Greenspan appeared on a panel with Wim Duisenberg, the head of the European Central Bank; Eddie George, governor of the Bank of England; and David Dodge, head of the Bank of Canada.