At issue are changes MBIA sought to make to the terms of some of its bonds to eliminate the risk that it might be considered in default if a troubled unit were put into rehabilitation or liquidation by New York regulators.
Bank of America countered with an offer to buy the bonds, saying it believed the changes would increase the risk of MBIA's insurance unit being placed in rehabilitation or liquidation, which could jeopardize all policyholder claims.
On Thursday, Bank of America said it had purchased $136 million of senior notes in that tender and issued a default notice over the attempt to change terms.
The bank claims in the lawsuit that the consent solicitation was the latest of MBIA's "premeditated and subversive actions" since 2008 to benefit executives and stockholders to the detriment of Bank of America and other policyholders.
In the lawsuit, filed late on Thursday, Bank of America alleged that MBIA illegally interfered with its tender offer and asked for the consent solicitation and amendment to be declared invalid. The bank also is seeking punitive and other damages.
MBIA spokesman Kevin Brown said: "Like its purported notice of default, Bank of America's latest lawsuit is meritless and we will respond to both accordingly."
MBIA shares fell 6.7 percent to $7.95 Friday on the New York Stock Exchange.
The legal wrangling is a major cloud hanging over both companies, which have struggled to recover from mortgage-related troubles from the financial crisis.
MBIA claims that Bank of America owes it billions of dollars over soured mortgages that it wants the bank to buy back. Bank of America says the insurer will likely owe it billions over certain credit default swap transactions.
MBIA and Bank of America were in court this week on pre-trial motions in a 2008 case the bond insurer brought against Bank of America's Countrywide Financial unit, accusing the lender of misrepresenting the quality of loans underlying mortgage-backed securities it insured.
MBIA claims the bank should be liable for refusing to buy back defective loans.
The two are also awaiting a decision by a New York judge over whether the state insurance department was right to approve MBIA's 2009 split into two units.
Bank of America claims it was harmed in the restructuring when $5 billion was transferred out of the MBIA unit that insures risky mortgage debt and into a new unit that guarantees municipal bonds. The judge must rule on whether to annul that split.
The newest case is Bank of America Corp. v MBIA Inc, New York State Supreme Court, 70444/2012, County of Westchester.
Writing by Ben Berkowitz; additional reporting by Rick Rothacker; editing by Bernadette Baum, Matthew Lewis and Carol Bishopric