D.C. Auditor Matthew s. Watson said yesterday that the District government "is not capable" in the immediate future of running a controversial workers' compensation program that pays benefits to workers injured on the job.

Citing as reasons the city's "financial ills," legal uncertainties and difficulties in training D.C. employes to take over the federal program, the auditor said any attempt to take charge should be put off until the fiscal year that begins in Octber 1981.

The program is currently administered by the U.S. Department of Labor. D.C. business leaders have been lobbying to reform the 50-year-old program because its costs -- borne by employers -- have jumped 600 percent since 1972. This rise in cost is driving some businesses out of town, they say.

Watson presented his findings in an eight-page report delivered to City Council member Wilhelmina J. Rolark (D-Ward 8). Rolark had requested that Watson study problems that would arise if the District assumed control of the program as proposed in legislation by council member Willie J. Hardy (D-Ward 7).

The Greater Washington Board of Trade, which worked closely with Hardy in drafting her legislation, attacked the report as an unfair analysis.

The injured workers program, called workers' compensation, requires that each employer doing business in the District carry private insurance against injuries to workers. Under the law, workers give up their right to sue for negligence in any job-related accident. They are guaranteed disability payments at about two-thirds of their salary under a no-fault system.

The District currently pays more than $820,000 a year to the federal government to administer the program. This money covers the cost of federal claims examiners, clerical workers and office space.

Watson estimated that it would cost the District about $1.1 million a year to administer the program efficiently. Even though Hardy's bill would require businesses to pay this administrative expense, Watson said, "I do not believe that the District could be ready to assume the program" in October, as proposed by Hardy.

Part of the reason, the report said, was that federal workers who now run the program "expressed an unwillingness to transfer to the District government."

"Further, given the financial ills of the city, it would not be wise for the District to adopt any new program," Waston said. He said such a program "would entail costs above the present level and would test the resources of other District programs that would be directly affected. . . ."

John Tydings, board of trade executive vice president, said that Watson miscalculated the benefit to the District of eliminating the $820,000 D.C. payment to the federal government for administering the current program.

"The fact that the [administrative costs of the] program is paid for by private employers for the first time represents [under the Hardy bill] a significant burden shift from taxpayers," said Tydings.

He also said it was unfair to suggest that the District would have to hire the same number of employes as the Labor Department now employs to administer the program because the District would not assume responsibility for the estimated 12,000 open cases being handled by federal officials.