In his prepared remarks, Mr Greenspan said that although in the short term "much economic activity virtually ground to a halt," the long-term economic prospects "have not been significantly diminished by these terrible events".
Mr Greenspan warned that the shock of September 11 "by markedly raising the degree of uncertainty about the future, has the potential to result in a pronounced disengagement from future commitments."
'Liquidity boost worked'
But Mr Greenspan offered reassurance that the initial disruption to the financial system - as some banks were unable to pay their obligations following the disruption to Wall Street - has now eased following a massive infusion of funds from the US central bank last week.
"The temporarily bloated balance sheet of the Fed is now shrinking back to normal," he told the Senate banking committee.
And - he added - "For the longer term prospects for continued rapid technological advance and associated faster productivity growth are scarcely diminished."
Consumers must spend
US Treasury Secretary Paul O'Neill, in his prepared remarks, told the Senate committee that all Americans can contribute to keeping the economy strong by going back to work and not cancelling any of their existing spending plans.
"Each and every American should know that by continuing to work and spend, they are doing their part to restore our nation and our economy in the wake of last week's attack," he said.
And he pointed out that America's productive capacity has not been fundamentally damaged.
"In the long term the economy remains sound," he concluded.
"Although the financial sector has been damaged, it continues to function. Moreover, the economy's productive capacity is fully intact, ready for whatever trials lie ahead."
The Bush administration is already discussing with Congress plans for further measures to boost the economy, including tax cuts and more interest rate reductions.
Both Mr O'Neill and Mr Greenspan warned against over-hasty economic reactions to the crisis.
"It is more important to be right than quick," Mr Greenspan pointed out.
Mr O'Neill said that he would wait for several weeks to see how much extra stimulus the economy might need after things had settled down.
But he said the administration was considering all possible options, although he hinted that he was considering cuts in business taxes to help boost the value of their company shares.
Backing the airline bail-out
Mr O'Neill strongly defended the Bush administration plan to bail-out the airline industry, which has announced thousands of job losses after passenger numbers plummeted.
He said that it was important to "socialise the costs" of airline safety, and possibly to "socialise the insurance costs" of airlines who need to insure against terrorism.
He rejected pleas from right-wing Republican Senator Phil Gramm, who asked for loans rather than grants to the airlines.
He said he favoured direct aid, because no insurance companies would want to write an open-ended policy covering terrorism.
"The idea of loan guarantees makes no sense," he stated.
And he said that urgent measures were needed to reassure the public and get people flying again.
Fears of recession
Despite Mr O'Neill's cautious optimism, many economists are warning that the tragic events of last week could trip the US economy into recession.
Economic conditions were already slowing down, with the Federal Reserve itself warning on Tuesday that there had been signs of a slowdown across many sectors and regions before the attacks.
And consumer confidence, which was already falling, is likely to be further affected by the wave of job cuts announced by the airlines, aerospace and tourism industries.
"There is a greater degree of uncertainty and stability will need to be restored," said Ian Morris, chief U.S. economist at HSBC Securities, who is predicting further rate cuts across the world.
David Jones, chief economist of Aubrey Langston said that the economy was already looking vulnerable, but that the US economic growth could now decline by up to 5% in the fourth quarter.