Mayor Walter E. Washington gave the City Council a setback yesterday in its plans for property tax relief by rejecting most of the $10 million in budget reductions that the Council had made to finance its tax-cut plan.

The mayor reinstated $4.9 million of the $5 million the Council had slashed from the city's welfare fund and $2.3 million of the $2.5 million the Council had cut from the funds for executive level pay raises.

He also reinstated to the two-year supplementary spending package $704,100 the Council had cut from the city's street lighting budget. Without that money, the city would have been forced to reduce the number of street lights turned on in some areas of the city.

The Council will have to override the veto if it intends to restore the cuts and finance a proposed $16.6 million property tax relief plan that would save every city homeowner $100. Council Chairman Sterling Tucker said through a spokesman that the Council would reconsider the budget next week. Tucker expects some of the reinstatements made by the mayor to be upheld, the spokesman said.

The mayor's action came on a proposed $70.4 million dollar spending package that contains supplementary spending for fiscal years 1977 and 1978.

Last week, the Council slashed $10.1 million from the $26.3 million operating budget supplements proposed by the mayor and $17 million from a $44.1 million capital programs budget supplement.

In the capital programs area, the mayor agreed with the Council's rejection of $17 million to renovate Glenn Dale hospital, the city's home for the chronically ill. He also concurred with the Council's decision to spend $27.7 million to begin building a proposed $110 million civic center in the Mount Vernon Square area downtown. Neither of those actions directly affect the property tax plan, however.

The largest and most controversial operating cut made by the Council and restored yesterday by the mayor was in the city's $100 million welfare fund, which provides money for the Aid to Families with Dependent Children and General Public Assistance programs.

Citing an estimated $16 million in annual losses due to erroneous payments, the Council cut $5 million from the fund. Making the cut would serve, as an incentive to the Department of Human Resources, the Council said, to remove ineligible persons from the rolls.

In the face of continuing problems with erroneous payments in DHR, the Council had hoped to compel the agency to cut down its payment error rate by giving DHR less money to spend. With $5 million less in the welfare fund, the Council argued, DHR would be forced to save at least $5 million by getting ineligibles off the rolls.

The mayor argued yesteday that if that were done, it could jeopardize DHR's previous plan to use the money saved for a 5 per cent increase in benefits to AFDC and GPA recipients rather than to compensate for budget reductions.

If the $2.5 million were not allocated for the executive pay raises as proposed by the council, the mayor said, some programs might have to be curtailed in order to finance the pay raises, which were mandated by congressional action earlier this year.

The mayor has proposed his own property tax-cut plan that would reduce by 7 cents the city's tax rate of $1.83 per $100 of assessed evaluation. That plan, which would save the owner of a typical city home $35, would be in effect for only one year.