Mayor Walter E. Washington signed into law yesterday a bill passed two weeks ago by the City Council that will give tens of thousands of District of Columbia residents an extra 30 days to pay their water bills if the bills total more than $75.

The mayor's decision came after more than a week of agonizing debate within his administration about the ability of the city's understaffed, antiquated and poorly managed water revenue division to implement a program designed to relieve city residents who have been receiving unexpectedly large, and in many cases incorrect, bills since early June.

When the City Council passed the relief legislation last month, members expressed a hope that the water revenue division would establish a system allowing residents to pay large bills in stages rather than all at once.

But the Council gave the mayor latitude to set up the payment schedule, and he decided yesterday that the Council's proposed partial payment plan was impractical because the water revenue division's bureaucracy and billing machinery could not cope with such payments.

As a compromise between the Council's desire and the bureaucracy's recommendation that the legislation be vetoed, the mayor decided to give residents an additional 30 days - beyond the month they already have - to pay water bills.

After signing the legislation late yesterday afternoon, Washington said he recognized that large and unexpected water bills have become "a serious problem" for many city residents.The mayor added that "we are working toward improvement of the (billing) system."

The new law also gives city water customers another important measure of relief. In the past, customers who wanted to contest water bills had to pay them first and wait for a refund if their bill was later found to be too high. In the future, they do not have to pay contested bills until the water department has reviewed them and determined whether a bill needs adjustment.

The city has a total of 120,000 residential and commercial water customers. According to water revenue division officials, approximately 60 per cent of the bills sent out since June 1 were for more than $75. The officials said that the first 40,000 of those bills averaged $110.

In fact, some city residents have received bills for huge amounts of money. At least one homeowner received a bill for $2,000 that even water revenue division officials conceded must have been incorrect.

If a water customer does not pay a bill within the new 60-day deadline, a 10 per cent late fee is charged. If the customer still does not pay, he is faced with a cutoff of water service. The city does have a hardship provision for customers who can demonstrate that they simply do not have the money to pay bills.

But water division officials could not explain yesterday what guidelines are used to determine when a hardship exists. They said some customers' water is cut off.

In a city not known for having a particularly efficient bureaucracy, the water revenue division of the D.C. Department of Environmental Services has for years been an unusually troublesome agency.

Herbert Tucker, the department's present director, acknowledged recently that he found "mass confusion" in the water revenue division when he was appointed to the job last year.

Tucker said the division's problems go back to 1970 when his two top officials retired within months of each other, leaving the division in the hands of inexperienced supervisors who had no written operating procedures to guide them.

Tucker said the division still does not have written procedures but said, "We're working on them."

Between 1970 and 1975 problems within the water revenue division mounted. Tucker said, leading to a City Council mandate in both 1975 and 1976 that the division mail all its bills by May 1 in each of those years.

"The bills went out, but we had trouble in crediting the accounts because of the volume of payments that were returned just as we had mailed them out - all at once," Tucker said.

The mass mailings created even more problems for the division, which is only partially computerized, and led to a decision this year to skip the usual twice-yearly billing schedule for all residential customers and begin a once-a-year schedule.

While the division bureaucracy may be better able to cope with only one mailing per customer per year, many residential customers at first were surprised and then outraged at receiving bills twice as high as usual yet still payable within 30 days.

Customers began complaining to Council members who passed two weeks ago the legislations signed by the mayor yesterday.

In addition to the 12-month billing schedule that results in such large bills, water revenue division officials admit that they make mistakes.

Council member Marion Barry (D-at-large recently made a list of 29 water customers who thought their bills were unusually high. The water revenue division found that six of the 29 had been overcharged.

Division officials suggest, however, that many city residents who think their bills are too high may have received correct bills. The officials point out that water rates have increased substantially over the past year, leading to higher bills for all users.

Tucker said the division's bureaucratic problems may be remedied when a master record of customers is updated properly and a new computerized billing system is in place. He said this will take at least two years.