The Federal Reserve is fighting a subpoena from lawyers in a civil lawsuit who want the central bank's chairman, Ben Bernanke, to testify about conversations he had with Bank of America Corp. executives before the lender completed its purchase of Merrill Lynch & Co.

The three-year-old class-action suit alleges that the Charlotte, N.C., bank and Kenneth D. Lewis, then its chief executive, misled shareholders about ballooning losses at Merrill before the $19.4 billion acquisition was approved. The government provided $20...