Greenspan's worry, shared by chief White House economist Gregory Mankiw, is that too much of the mortgage market is concentrated in Fannie Mae and Freddie Mac, which could trigger a crisis if interest rates rose suddenly and unexpectedly, causing the mortgage giants to have trouble making payments on their debt.
Greenspan called for limits on how much debt the two institutions could issue and how many mortgages they could hold.
Mankiw warned in a column yesterday in the British newspaper the Financial Times that Fannie Mae and Freddie Mac were "a source of systemic risk for the U.S. financial system."
The sheer size of their debt - about $1.5 trillion combined - and their dominant role in the housing market is raising concern that a crisis at either institution could undermine U.S. financial markets and trigger at least a temporary freezing of the mortgage market. Fannie Mae and Freddie Mac back almost 57 percent of all residential mortgages.
To avert such a collapse, Congress might have to authorize a bailout - and taxpayers would have to foot the bill.
Fannie Mae and Freddie Mac issued statements taking issue with Greenspan's comments. The heads of both institutions are due to testify today before the Senate Banking Committee in a second day of hearings on the issue.
"We, of course, disagree with most of his conclusions, but appreciate that he has now made his strongly held views public," Jayne Shontell, senior vice president for investor relations at Fannie Mae, said in a lengthy written statement.
Greenspan acknowledged that Fannie Mae and Freddie Mac have managed their risk well in the past, and he emphasized that there didn't appear to be an imminent problem.
The institutions engage in complex financial transactions known as hedges to reduce the risk posed by sudden changes in interest rates.
But financial market history has shown that even the best minds in finance can be brought down by unforeseen developments.
Greenspan argued that the risks were excessively concentrated in large institutions that were potentially subject to human error.
He also cited a Federal Reserve study that concluded that Fannie Mae and Freddie Mac benefit from an implied subsidy from the government, because most investors assume they would be rescued in a crisis. That perception allows the institutions to borrow money more cheaply and to pay higher prices in the market for mortgages, squeezing out potential competitors.
Contact reporter Ken Moritsugu at firstname.lastname@example.org.