A massive effort by the Federal Reserve system to save the U.S. economy from a deep depression has succeeded in softening the impact of the current recession, said Richard Fisher, president of the Dallas Federal Reserve Bank, Tuesday.

"We have succeeded in pulling the economy back from the brink," Fisher told local bankers and officials in Lubbock, Texas, during a speech. "We've come back from the abyss."

Economic indicators, including rallying stock markets and rising consumer confidence, are showing early signs of improvement. Fisher said there are more corporate bond issuances, and the banking system seems healthier as well, he added.

"The bankers are depending less on us for term lending," said Fisher. "The banking community has been somewhat repaired."

Fisher said he forecasts not a "v-shaped" or "u-shaped" recovery, but "very slow" natural growth.

Many uncertainties remain: the bankruptcy filing of General Motors (GM) could have a "dampening effect" on the recovery, he told reporters after the speech. "It's going to slow us down, but it's not a fatal blow."

Energy prices, which have acted as a sort of stimulus to consumers since they fell from record heights months ago, are beginning to rise again, prompting questions on whether they could also harm economic recovery. Fisher said the situation is still unclear, as prices were rising, but natural gas prices, which have a big impact on consumers, remain low.

Rising treasury yields have resulted in increasing mortgage rates, prompting fears the élan toward recovery in the housing market could stall. But Fisher said it was not clear whether the rising yields reflected mostly the current reactivation of the borrowing markets, or whether they were a sign of the U.S. government's borrowing needs.

Fisher said now that the banking system seems to be coming back from the edge of catastrophe, the U.S. should design a new regulatory system for banks that would "better define what the parameters are."

"We have to define a new fence line," he said. "More clearly defined, and I hope, simplified. We can't create a system where we reward losers."

-By Angel Gonzalez, Dow Jones Newswires; 281-536-3064; angel.gonzalez@dowjones.com