Morgan Stanley, the sixth-largest U.S. bank by assets, said it may be sued by American International Group Inc. over mortgage-backed securities that the insurer bought before the financial crisis.

AIG purchased $3.7 billion in mortgage pass-through certificates that were sponsored or underwritten by Morgan Stanley in 2005 through 2007, the New York-based investment bank said today in a regulatory filing. AIG terminated an agreement that had given it more time to bring claims, and the pact will end Nov. 7, according to the filing.

AIG, which repaid a government bailout last year, sued Bank of America Corp. in August 2011 over $10 billion in losses on mortgage-bond investments, saying it was the victim of a “massive fraud.” Morgan Stanley has set aside $549 million for litigation in the first nine months this year, up from $381 million in the same period last year.

“The company expects future litigation accruals in general to continue to be elevated,” Morgan Stanley said in the filing. “Changes in accruals from period to period may fluctuate significantly given the current environment regarding financial crisis-related government investigations and private litigation affecting global financial services firms, including the company.”

AIG was bailed out by taxpayers in 2008 after the New York- based insurer was overwhelmed by losses on property bets. Matt Gallagher, a spokesman for AIG, declined to comment. Charlotte, N.C.-based Bank of America has disputed the insurer’s claims.

Morgan Stanley helped advise the U.S. government on its rescue of AIG and was one of top underwriters as the U.S. divested its majority stake through public offerings. It also helped AIG dispose of a stake in reinsurer Transatlantic Holdings Inc.

–With assistance from Noah Buhayar in New York. Editors: David Scheer, Dan Reichl