Mortgage-bond investors are urging the government to stop banks from saddling them with the costs of probes into sales of the debt.

The Association of Mortgage Investors, whose members include DoubleLine Capital LP and AllianceBernstein Holding LP, made the plea to U.S. Attorney General Eric Holder in a letter last week. The missive followed reports that Bank of America Corp. and Citigroup Inc. were separately attempting to negotiate multibillion dollar accords with the U.S. that would grant credits to the lenders for changing loan terms for homeowners.