District government officials, noting that they had located unpaid water bills from the nineteenth century, announced plans yesterday to begin operating an extensive computerized financial management system on Monday.

"The new system will bring financial discipline to the city," said Colin F. S. Walters, assistant city administrator for financial management.

Although District officials hailed the system as the answer to many of the city's bookkeeping problems, they were careful to tell a group of reporters the $9 million centralized system will undergo a rough initiation period.

"I trust that when you hear that the system has broken down, you'll remember that it's a huge enterprise," Walters said, pointing out that the city operates a $8 million daily budget.

The computer system, which will link District government agencies across the city, is designed to respond to criticism from the General Accounting Office and members of Congress who have consistently found the city's books poorly maintained and often unauditable.

Furthermore, District officials hope the system will bring the city's financial standing to a point where it can issue municipal bonds by the summer of 1981.

The city government would then be able to borrow money at rates well below what it must pay to borrow from the U.S. Treasury -- currently 9 percent. The poor state of the city's books bars it from issuing bonds.

The computer program has been developed by the Temporary Commission on Financial Oversight, a panel made up of members of Congress and the city government.

Their mission is to improve the city's financial planning and control systems and to get the city's books into shape so that full scale audits can begin with the 1980 fiscal year. In the meantime, Arthur Andersen & Co. will conduct a partial audit of the city's fiscal 1979 records.

Between 2,500 and 3,000 city workers have been trained to operate the computer terminals, although ultimately the system could lead to cuts in the District government's work force. "There will be some personnel economies after the shakedown period of a year or more," said Bruce W. Rohrbacher, executive director of the commission.

The system will enable city officials to obtain data, updated each night, which will list the government's transactions and purchases. Further, it will permit agency managers to determine how much time employes have spent on certain tasks.

Ultimately, all the city's billing will be conducted through the computer system, as will the District's parking ticket collections.

American Management Systems, Inc., a private computer concern based in Arlington, designed the system under a $6 million grant. The company also designed a similar system for New York City.

Mayor Marion Barry Jr. repeatedly cited financial management as a cornerstone of his administration while campaigning for the office and is pinning much of his hopes for the city's "fiscal autonomy" on the success of the computerized system.

On Feb. 1, Barry is scheduled to present the City Council with a detailed report of the progress of modernizing the city's budgetary system. Arthur Andersen & Co. will aid in the preparation of that report, in an effort joined by Lucas Tucker & Co.