(Adds other banks' share offerings)

NEW YORK, May 19 (Reuters) - Bank of America Corp (BAC.N: Quote, Profile, Research), ordered by federal regulators to plug a $33.9 billion capital shortfall, priced roughly 800 million shares at $10 each on Tuesday, a person familiar with the transaction said.

The largest U.S. bank by assets declined to comment. The person was not authorized to speak because terms of the sale are not public.

The sale price is 11.1 percent below Bank of America's $11.25 closing price on Tuesday. Bank of America shares initially fell several percent in after-hours trading, but later recovered to $11.18.

A sale of stock may help Bank of America raise capital, after regulators told Chief Executive Kenneth Lewis the bank needed to bolster its finances following a government "stress test" of its ability to handle a deep recession.

Ten of the 19 large U.S. banks that underwent such tests were told this month to raise capital, with Bank of America's $33.9 billion shortfall being by far the largest.

An offering by Bank of America would come on the heels of large share issuances by other banks ordered to raise capital. This includes offerings of $8.6 billion by Wells Fargo & Co (WFC.N: Quote, Profile, Research) and $4 billion by Morgan Stanley (MS.N: Quote, Profile, Research).

Several banks found to have no capital needs sold stock this month to position themselves to repay taxpayer money taken from the federal Troubled Asset Relief Program.

Bank of America has taken $45 billion of TARP money, including $20 billion in a bailout to help it absorb Merrill Lynch & Co, which it bought on January 1.