Bank of America Corp said on Thursday it may swap 200 million common shares for existing preferred stock, moving it more than $2 billion closer to plugging a $33.9 billion capital shortfall.

The largest U.S. bank announced the exchange offer a day after it said it had raised close to $26 billion of equity capital this month, including $5.9 billion from another swap of common shares for preferred stock.

Bank of America said it might issue 564 million shares from similar swaps, and that Chief Executive Kenneth Lewis owns 86,000 preferred shares eligible for the latest swap. Two hundred million common shares are worth about $2.18 billion, based on the bank's Wednesday closing price.

The bank was among 10 large U.S. lenders told by federal regulators this month to raise capital after government stress tests of their ability to handle a deep recession.

Bank of America's $33.9 billion hole was more than twice as large as any rival's. The bank originally expected to raise just $17 billion by issuing common shares, as well as $10 billion from asset sales and $7 billion from other actions, including improved revenue streams.

According to The Wall Street Journal, the Federal Reserve is limiting the extent to which banks may fill capital holes through increased revenue. It said Bank of America may use only $1.7 billion of expected excess revenue, rather than $7 billion, for this purpose.

Bank of America said it had about 7.92 billion common shares outstanding as of May 26, including roughly 1.5 billion issued this month.

The bank declined to comment on the report, or on Lewis' plans to swap his preferred shares.

Bank of America said its exchange offer expires on June 24. Shares of the bank fell 7 cents to $10.84 in morning trading on the New York Stock Exchange.

(Reporting by Jonathan Stempel, editing by Dave Zimmerman)