The Federal Reserve is closely watching for signs the European sovereign debt crisis could derail a fragile U.S. economic recovery, a top Fed official said on Thursday.

One risk to the outlook ... is the fallout from potential sovereign debt default as conditions continue to deteriorate in Greece and other countries, St. Louis Federal Reserve Bank President James Bullard told an audience at Washington University's Olin Business School.

The euro and stocks worldwide have fallen over the last three days over worries that Greece's debt crisis was spreading to other weak euro zone economies. Greece is preparing to adopt harsh austerity measures as part of a European rescue package aimed at staving off a default on its debt.

Bullard's remarks are the first direct indication that European debt worries are a concern for the Fed, which renewed its vow to hold benchmark U.S. interest rates exceptionally low for an extended period at a meeting in late April.

European turmoil is by definition a factor in Fed deliberations about monetary policy, said Bullard, a voter this year on the Fed's policy-setting panel.

Of course we're always looking at all developments globally when we're trying to make monetary policy, he told reporters after his speech.

The Greek situation would be no exception to that ... For now it's just something we're watching very closely, he said.

Bullard raised the possibility Greece might have to restructure its debt, for example by delaying payments, but said that process is familiar from the experience of other countries.

Restructuring debt, if it does come to that, you can live through it ... it's not pleasant, he said. It does create a lot of volatility.

Asked why policy-makers failed to foresee the Greek crisis, Bullard said Greece had hidden the extent of its debts.

Frankly Greece ... lied about how much they were borrowing, he said. It wasn't a small discrepancy, either.

Bullard said that as far as he knows other nations whose fiscal situations are in question, such as Portugal, Spain, and Italy, have not misrepresented data.

Bullard declined to respond specifically to whether he is considering dissenting against maintaining the Fed's low-rate pledge despite signs the recovery is gaining traction, as one other policy-maker has, but suggested that is not likely.

It's largely a consensus organization at the end of the day and I respect that, he said.

Pressed on whether he thinks that based on positive trends in the economy it was time to lift the extended period language, Bullard said, No, I don't think so. I've just tried to stress that it's important to have a .... policy that emphasizes that everything depends on how the economy evolves ...

Bullard said good news outweighs bad news as the U.S. economy crawls back to health from a deep recession.

We're well into our recovery process, he said.

Rebounding manufacturing and slowly improving labor markets are among indications of improvement in the United States, he said, adding he expects employers to continue to add jobs in the spring and summer.

Inflation remains low, he said.

For now ... inflation remains pretty subdued. To the extent that we have inflation risks, it's a couple of years into the future, he said.

(Reporting by Mark Felsenthal; Editing by James Dalgleish)