The District of Columbia government is feuding with the federal government over $22 million in charges for housing local prisoners in federal jails, according to a recent General Accounting Office report.

The GAO report says the city has accumulated the debt to the Federal Bureau of Prisons since 1976. City officials acknowledge that most of this money is owed, but say that the federal government has not substantiated its claim that $22 million is the amount due.

The most serious problem, the GAO report found, involves about $7 million in billings from 1976 to mid-1981 that remain unaudited or are in dispute. City officials said the District has not paid these because it found duplicate bills or could not find records on the prisoners concerned. The city also disputes interest charges the bureau applied to the unpaid bills.

More recent billings have been smoother, though not flawless, because of changes in the payment system, the GAO report said.

GAO still found the federal and local agencies blaming each other for problems in getting differences resolved, however. Each agency says the other has not provided proper documentation for its claims and has not responded to initiatives to resolve the disputes, for example.

". . . . the tone of the comments from both agencies caused us some concern," the report said. "Unfortunately, this mutual fault-finding reflects the same attitude that has been a barrier to solving the problems of disputed billings."

Representatives of the D.C. Department of Corrections and the Federal Bureau of Prisons yesterday vowed to stop squabbling over who was to blame for past errors and to get the matter resolved quickly. In a hearing held by a House Government Operations subcommittee, the city and federal representatives said they would try to reach an agreement by September and would report back to the subcommittee on their progress.

The city has more prisoners in federal facilities than other states--about 1,300 prisoners compared to 945 for all the states and territories combined--because of overcrowding in District prisons and because of a special relationship between the District and the federal government that allows the city to send prisoners to federal facilities as well as city prisons.