District of Columbia officials have found that a $6 million audit completed earlier this year, the first ever of the city government, is in many instances unusable because the private auditors used on accounting method that is significantly different from the city's own.

D.C. Budget Director Gladys W. Mack said yesterday that there are "hundreds" of discrepancies between the City's books and expenditures reported by the auditor, Arthur Andersen & Co. and Lucas, Tucker & Co.

District government officials say they still do not know precisely how much various city departments spent during the 1980 fiscal year. The audit shows the D.C. Fire Department underspending its budget by $4.3 million, for example, while the city says the department actually overspent its budget.

D.c. Controller Al Hill and his aides are currently examining the auditors' records in an attempt to resolve the discrepancies -- a process that could take weeks or months, officials said.

Because of the discrepancies, the District was not able to report its actual 1980 departmental spending figures to Congress last month when it submitted the city's propsosal 1982 budget.

"We're concerned," said Philip C. Dearborn, financial adviser to Mayor Marion Barry. "It's important that we have all this information as we look at our budgets for 1981, '83."

Mack said, "Even after the audit, we do not have sufficient management data, and we are having to make that data cleaner."

The auidit was ordered by the Temporary Oversight Commission established by Congress to improve the city's accounting practices. Half the $6 million spent to pay for the work was paid by the city, and the other half by Congress, as part of a $38 million program to bring the city's bookkeeping practices in line with accepted accounting principles.

City officials said the discrepancies and the audit's lack of information on expenditures within the individual departments might be attributed to the fact that it was the first-ever audit of the city's books, as well as problems within the city's own $20 million computerized accounting system, known as the FMS (Financial Management System), that was mandated by the congressional commission.

"I would be very disappointed if we had this same kind of problem again," said a city financial official who asked not to be named. "Perhaps you can excuse it because it's the first time, but this really shouldn't happen under a well-run accounting system."

"There is not a yes or no answer" to the question of whether the audit justified the $6 million cost, another official said. "The answer to that question lies in what the auditors thought they were supposed to audit. A lot of the data they had to work with was not reliable. I guess we have to accept what they came up with."

The Arthur Andersen & Co. officials who worked on the audit could not be reached for comment yesterday, and a representtive of Lucas, Tucker declined to comment.

The audit does not include figures on spending within the agencies -- for example, how much the police department spent on gasoline, or how much the planning department spent on office supplies.

The auditors did examine many of these expenditures, officials said, but drew heavily for their information on the computerized FMS accounting system, which underwent serious problems throughout much of the fiscal year.

"We never had reliable information out of the system all year," Mack said. "We only started getting some information out last March.It could be that this was the best the auditors could do with the data that was available."

"I guess they didn't consider [spending by departments] within the scope of their audit," Dearborn said of the auditors. "We're to sort that out now. They came up with totals, but we're now left with the problem of breaking the totals down to individual items."

In the process of the audit, he said the accounts "move theings around that changed the totals" already existing within the FMS system.

Before the city can know exactly what its agencies spent last fiscal year, said Dearborn, it must allow for all the changes made by the auditors. The city "certainly would have expected" to know the firm totals in time to submit them to Congress with the 1982 budget last month, he said.

To reconcile the figures, Mack said, Hill and his aides have begun examining records kept by the accountants during the preparation of the audit, and must record "hundreds of transactions," a process likely to take more than a month.

"In the past we've developed our budget request based on the actual spending," Mack said. "But that information just is not developed at this point."

The spending discrepancy within the fire department, for example, has been traced to the way the auditors listed the department's share of pension funds. "We're pretty sure that's the culpit in this case," she said.

The city officials, as well as staff members of the oversight commission, emphasized that they were satisfied with the audit insofar as it reliably reported for the first time total city spending and revenue collection, and gave a clear picture of the city's over-all financial condition as the fiscal year ended last Sept. 30.

The city hopes to use the audit in its attempt to solve an accumulated budget deficit by entering the municipal bond market. Barry is asking Congress for permission to sell $194 million in bonds to finance the debt.