U.S. bank earnings reached a more than four-year high in the third quarter, but regulators are warning that the industry faces challenges that include the risk of the European debt crisis washing up on U.S. shores.

Martin Gruenberg, acting chairman of the Federal Deposit Insurance Corp, said on Tuesday that U.S. banks have limited direct exposure to Europe, but there is a risk of contagion if the situation gets worse.

Close attention is being paid to what we see as the possible avenues for contagion, particularly in regard to the derivative markets, he said at a news conference.

Gruenberg said U.S. banks had significantly improved their capital and liquidity positions since the 2007-2009 financial crisis and that regulators continue to make sure this foundation is sound.

FDIC staff said that, with regard to derivatives, regulators are working with banks to make sure they understand their counterparty risk.

I would say this is no surprise to these institutions now. This has been a subject that has been developing over several quarters and they have had plenty of time to adjust their positions, which they have, said John Corston, associate director of the FDIC's Systemic Financial Companies Branch.

On Tuesday, the FDIC released its latest quarterly report, which showed that the industry had earned $35.3 billion in the third quarter, the most since the second quarter of 2007.

Third-quarter earnings rose $11.5 billion from a year earlier and were up $6.7 billion from the second quarter.

The industry continued to boost profits, however, by setting aside less to guard against losses from bad loans.

Banks set aside $18.6 billion in the third quarter for losses, which is 47 percent less than a year ago.

The FDIC again warned that the increase in quarterly earnings would be difficult to maintain because revenue growth remains slow.

Net operating revenue rose $864 million, or less than 1 percent, in the third quarter from a year earlier.

Loan balances grew by $21.8 billion in the third quarter, the second quarterly increase in a row, but that amount will have to increase if bank profits are to continue on the upswing.

After three years of shrinking loan portfolios, any loan growth is positive news for the industry and the economy, Gruenberg said, but the lending growth we are seeing remains well below normal levels.

There were slight increases in commercial and residential housing lending.

The report showed that the health of bank balance sheets continued to improve in several areas.

For instance, the amount of delinquent loans on banks' books, those 90 days or more past due, dropped for the sixth consecutive quarter.

In addition, the losses banks are taking on bad loans continued to drop. In the third quarter these charge-offs totaled $26.7 billion, or 39.2 percent less than a year ago.

While economic difficulties remain, higher capital levels, increased liquidity and lower losses signal a positive trajectory as the banking industry continues to gain strength, Jim Chessen, chief economist at the American Bankers Association, said in a statement.

The FDIC report also showed that skittish investors continue to seek a safe place to park their funds as financial markets remain volatile.

Deposits grew by $234.5 billion in the third quarter, a 2.4 percent increase from the previous quarter.

(Reporting by Dave Clarke; Editing by Dave Zimmerman, Lisa Von Ahn and Steve Orlofsky)