(Adds comments from Q&A)

NEW YORK, Feb 17 (Reuters) - Former U.S. Federal Reserve Chairman Alan Greenspan said on Tuesday the current global recession will “surely be the longest and deepest” since the 1930s and more government rescue funds are needed to stabilize the U.S. financial system.

“To stabilize the American banking system and restore normal lending, additional TARP funds will be required,” Greenspan said in a speech to the Economic Club of New York. The U.S. Treasury’s Troubled Asset Relief Program designed to help bail out banks has been partially successful, he said.

Despite his prognosis on the current downturn, Greenspan said the pace of economic deterioration “cannot persist indefinitely.”

He reiterated, however, that a housing recovery is a necessary condition for the end of the financial crisis, and said that “the prospect of stable home prices remains many months in the future.”

The stock market, meanwhile, is being suppressed by “a degree of fear not experienced since the early 20th century,” Greenspan said. “Certainly by any historical measure, world stock prices are cheap. But as history also counsels, they could get a lot cheaper before they turn.”

A recovery in the equity market driven by lessening fear could be “a seminal turning point of the current crisis,” he said.

Citing the Japanese experience of the 1990s, Greenspan said U.S. authorities need to assure the repair of the financial system before major fiscal stimulus takes hold.

“Unless we are successful at that, in my judgment, the positive impact of a fiscal stimulus will peter out after its scheduled completion,” he said.

He said the real test of fiscal stimulus is whether it “primes the pump” for private demand.

Greenspan said the Federal Reserve’s myriad emergency lending programs and the Treasury’s TARP funds have the potential of being unwound eventually without leading to inflation or great cost to the taxpayer.

He warned, however, that politics could be an obstacle.

“At the first signs of stabilization and a flattening of the unemployment rate, I presume the Federal Reserve will start to rein in much of its credit extension,” Greenspan said.

“However, Congress is likely to strongly object to any tightening of credit prior to full employment being restored. Policy reversals on the fiscal front are nearly certain to meet stiff resistance,” he said.

The U.S. Treasury will have to heavily issue debt to fund its stimulus package, and while at the moment the Treasury is having no difficulty finding buyers for it, there is a limit to the expansion of the federal debt, he said.

Greenspan, a proponent of self-regulation, said he was “deeply dismayed” when in August 2007 the premise that firms had the enlightened self interest to monitor their own risk exposure “failed.”

“I see no alternative to a set of heightened federal regulatory rules for banks and other financial institutions,” he said.

“Even with the breakdown of self regulation, the financial system would have held together had the second bulwark against crisis, our existing regulatory system functioned effectively. But under crisis pressure it, too, failed,” Greenspan said.

That said, he still believes self-regulation is a first line of defense for market effectiveness.

“We need not rush to reform. Private markets are imposing far greater restraint at the moment than would any of the current sets of new regulatory proposals.”

Answering a question after his speech on whether he would have done anything differently during his tenure as Federal Reserve chairman to try and prevent the housing bubble, Greenspan said, “I think it would be desirable to find a way to suppress asset bubbles.

“But I am skeptical that it can be done.” (Editing by Leslie Adler)