D.C. City Council Chairman Sterling Tucker, in a letter with strong political overtones, scolded Mayor Walter E. Washington yesterday for recommending a budget that Tucker said would add to the city's payrolls while failing to give top priority to the most vital public services.

Tucker, a potential rival to Washington in next year's mayoral election, bluntly told the mayor that his proposed budget for the 1979 fiscal year - which begins next Oct. 1 - was "a disappointment to the Council."

Tucker's letter comes at a time of increased political jockeying among Tucker, Washington and Council member Marion Barry (D-at large). All three are expected to run in next year's Democratic mayoral primary.

Tucker's criticism of the mayor would appear to be another move in a continuing effort by the Council chairman to separate himself from Washington, who was his running mate in 1974 but who is likely to be among his foes in 1978.

Two weeks ago, the mayor scored impressive political points with some potential voters when he unexpectedly outmaneuvered the Council by vetoing legislation that would have allowed immediate rent increases of 2 to 10 per cent for all apartments in the city.

Despite Tucker's criticism of the mayor's budget yesterday, the Council had almost two months to change it. During that time, the Council reduced the budget by only $15.1 million, cut the number of city employees by only 54 and made no changes that would greatly alter the way the city is run.

Asked why Tucker had written the letter, an aide explained that the mayor attached a letter when he submitted the proposed budget two months ago, so Tucker decided to attach his own letter explaining the reason for changes made by the Council.

Tucker said the mayor's proposed budget had not only sought to add to the size of the city's work force but also continued an upward creep in pay grades by adding to the number of highly paid administrative personnel.

Referring to the budget total and the Council's cut of 515 million. Tucker declared:

Far more extensive budget) reductions, which only an Executive can implement are required to bring long range city expenditure levels in line with realistic future revenue growth projections.

"The District can ill-afford to continue to allow city agencies to dictate the need for increasing levels of taxation on city residents without sufficient Executive guidance."

Tucker said an upturn this year in the city's tax collections permitted the mayor to submit a budget that "allows postponement of the inevitable major adjustment of expenditure priorities to meet realistic revenue of growth projections."

When the mayor submitted the proposed budget to the Council, critics contended it contained unrealistically high projections of revenue, including an expected 23 per cent rise in the assessed value of all real estate and a $17 million increase in the federal payment to the city, which has not been authorized. The present federal payment is limited to $300 million.

Tucker renewed the criticism in his letter, saying $35 million in expected pay raises remain unfunded and revenues from such sources as he stepped-up collection of parking tickets could fall $7 million to $10 million short of expectations.

"The Council expects that you will be addressing these unfunded expenses and soft spots in revenue projections." Tucker wrote, "and that you will be submitting shortly proposals for dealing with them without additional tax increases."

Tucker's letter arrived at the mayor's office late in the day, and there was no immediate comment.

Although the federal payment - which compensates the city for taxes owned property - is presently limited to $300 million the White House has endorsed an increase to $317 million.