Mayor Walter E. Washington reinstated yesterday two-thirds of the $15.1 million that the City Council had planned to cut from his proposed 1979 operating budget and strongly defended his fiscal and personnel policies as being responsible and prudent and constructive "througout the (10) years of my administration."

The mayor's action, which amounted to a veto of $10.1 million in proposed Council reductions, was laced with the political overtones of the current jockeying for position among Democrats before next year's mayoral election.

The mayor's veto was accompanied by a five-page message, much of which appeared to be a direct response to criticism of the mayor earlier this month by City Council Chairman Sterling Tucker.

Tucker had called the mayor's proposed $1.3 billion budget "a disappointment to the Council" and a budget that would increase the size of the city's payroll without giving top priority to some of the most vital city services.

Mayor Washington said the budget he presented to the Council "was a responsible and prudent budget. It provided the necessary spending authority to maintain basic service delivery and to take care of essential program commitments. I have been committed to constructive personnel policies throughout the years of my administration.

"Currently, the primary interest appears to be budget cutting without regard for programs or service delivery consequences, wherever this can be achieved without the influence of public pressure," the mayor said.

"I have placed top priority on improving service delivery and operating efficiently without raising taxes. Productivity means to our citizens that we are cutting red tape, eliminating waste, holding the line on taxes, providing better services and trying to make the District of Columbia a better place to live," he said.

The mayor's vetoes leave a surplus of about $6.3 million in the fiscal 1979 budget, and an additional $1.3 million is expected to be saved because the city probably will have less debt service than orginally anticipated.

The mayor did not directly propose how that $6.3 million should be used. But he appeared to be cautioning the Council to move slowly on plans for property tax relief.

Such caution apparently arose because any unspent money the city may have in fiscal 1979 would result from an increased federal payment, and some members of the mayor's administration feel Congress would not be willing to increase the federal payment if that increase is earmarked for local property tax relief.

The Council's two leading members, both of whom are expected to run for mayor next year, already had proposed rival plans for use of the anticipated $15.1 million in budget reductions. Council Chairman Tucker would have liked to use $10 million of the money for a rent subsidy program, while Council member Marion Barry (D-at-large) had suggested using $12 million for a comprehensive residential property tax and rent relief program.

Among proposed reductions that the mayor rejected yesterday were substantial cuts in the staffs of the Office of Municipal Audit and Inspection, the mayor's productivity in government program and the Public Affairs Office. The Council had planned to cut the Public Affairs Office staff in half and abolish the agency by name.

The Council also had removed from the budget $88,000 to fund the information office for the Advisory Neighborhood Commissions, the city's publicly supported experiment in grassroots government. The mayor restored that money to the budget.

Among the largest reductions proposed by the Council was $2.6 million less in payments to the Federal Bureau of Prisons for the care of city prisoners held in federal facilities. The mayor agreed that not all of the money would be needed but urged a reduction of only $1.8 million.