European sovereign debt woes are a risk to the improving U.S. economic outlook, St. Louis Federal Reserve Bank President James Bullard 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, Bullard told an audience at Washington University's Olin Business School.

The euro and world stocks 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 sovereign debt default.

Bullard raised the possibility of a debt restructuring, saying other countries have been through such restructurings before.

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.

Bullard's remarks are the first direct indication that European debt worries are a concern for the Federal Reserve, which renewed its vow to hold rates exceptionally low for an extended period at a meeting in later April.

A voter on the Fed's policy-setting panel, Bullard said good news outweighs bad news for the U.S. economy's path 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, said, adding that he expects employers to continue to add jobs in the spring and summer.

Inflation remains low, while unemployment remains high, 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.

Turning to financial regulatory overhaul legislation being debated in Congress, Bullard warned that proposals to audit the Fed's decisions on interest rates and monetary policy would be damaging. Reviews of monetary policy would lead to a 1970s-style period of volatility, he said.

(Reporting by Mark Felsenthal, Editing by Chizu Nomiyama and Padraic Cassidy)