NEW YORK — More trouble piled up for Bank of America Corp. on Monday, as American International Group Inc. sued it for more than $10 billion, saying the bank cheated it by selling residential mortgage-backed securities that were overvalued.

The suit comes on top of similar suits, which together put the bank in a precarious position, analysts say. The bank’s stock dove 20 percent, or $1.66, to $6.51.

AIG said Bank of America and two companies that were later gobbled up by the bank, Countrywide and Merrill Lynch, sold the insurance company $28 billion in securities backed by home mortgages between 2005 and 2007, at the height of the housing boom. It said it looked at more than 260,000 of the underlying mortgages, and found that the bank’s “stated metrics” for 40 percent of the securities were false.

In one case, a borrower said she had been the owner of a construction business for 25 years, which would have made her 10 years old when she took ownership, AIG said.

Bank of America denied the allegations, saying AIG was big enough and sophisticated enough to know the risks.

“AIG recklessly chased high yields and profits throughout the mortgage and structured finance markets. It is the very definition of an informed, seasoned investor, with losses solely attributable to its own excesses and errors,” Bank of America spokesman Lawrence Grayson said.

AIG spokesman Mark Herr shot back: “It is disappointing but unsurprising that Bank of America continues to attempt to blame others for its own misconduct. Investors, no matter how sophisticated, were entitled to rely on its numerous written representations about the securities it sold.”

AIG shares fell $2.52, or 10 percent, to $22.58.

In June, Bank of America agreed to pay $8.5 billion to a group of investors for selling them poor-quality mortgage securities. AIG’s suit is separate, but the company is raising questions about whether the settlement went far enough. On Friday, New York Attorney General Eric Schneiderman urged the judge to reject the settlement.