In an interview on ABC's "This Week with George Stephanopoulos," Greenspan said low inflation was a major contributor to economic growth and prices must be held in check.
"We are beginning to get not stagflation, but the early symptoms of it," Greenspan said.
"Fundamentally, inflation must be suppressed," he added. "It's critically important that the Federal Reserve is allowed politically to do what it has to do to suppress the inflation rates that I see emerging, not immediately, but clearly over the intermediate and longer-term period."
The U.S. central bank has lowered its benchmark interest rate three times since mid-September as a housing downturn, tightening credit conditions, and steep food and energy prices threaten to push the U.S. economy into recession.
But cutting rates can have the unwanted side effect of pushing up prices, so the Fed finds itself in a tricky position of trying to revive growth without spurring inflation.
Last week, U.S. data showed that wholesale inflation rose at the highest rate in 34 years, while consumer prices rose the most in more than two years.
Greenspan repeated his assessment that the probability of a U.S. recession had moved up toward 50 percent but noted that corporate America's debt levels were in good shape, which should help cushion the blow from tightening credit terms.
"The real story is, with the extraordinary credit problems we're confronting, why the probabilities (of recession) are not 60 percent or 70 percent," he said.
"Because of the decline in long-term interest rates for a protracted period of time, American business was able to fund a significant part of its short-term liabilities and take out low-cost, long-term debt, so the credit needs have not been all that large," he said.
Greenspan has drawn some criticism for keeping the trendsetting federal funds rate at a low 1 percent from June 2003 through June 2004, which some argue contributed to a housing bubble that is now bursting spectacularly.
Greenspan said real estate prices will stabilize only when the overhang of unsold new-construction homes begins to ease, and estimated that financial losses could be in the range of $200 billion to $400 billion as securities tied to failing subprime mortgages lose value.
He warned against any sort of government bailout plan for homeowners that interfered with the normal functioning of markets for home prices or interest rates, saying it would "drag this process out indefinitely." Offering cash to stricken homeowners instead would cause less long-term damage, he said.
"It's only when the markets are perceived to have exhausted themselves on the downside that they turn," he said. "Trying to prevent them from going down just merely prolongs the agony."