The D.C. City Council voted 7 to 2 yesterday to work to trim more than $26 million from Mayor Walter E. Washington's proposed 1979 operating budget for the District.

Chairman Sterling Tucker, who suggested that the Council take such a stance early in its consideration of the recently proposed $1.3 billion money bill, conceded that the total finally approved might be well of the $26 million target figure.

"(It) is likely to be between the $26.3 million (trim proposed) and what the mayor has proposed," Tucker said.

The Council's action marked the first time that it had set a specific goal this early in its review process. The budget it is considering is for the fiscal year beginning Oct. 1, 1978.

As a starting point, the Council proposed that most of the city's agencies and programs be reviewed immediately and funding for each be cut by 1 per cent.

The Council majority acted out of concern that the mayor's revenue expectations were on the optimistic side, and the money wouldn't be there to finance all the activities itemized in the budget. If it is, they noted, these funds could be used as a reserve for any program that could effectively use additional funding.

That goal of reducing the amount of mercy sought represents a desire among Council members to give city taxpapers some type of tax relief in the future.

Tucker said yesterday that he hopes that the Council can come up with additional property tax exemptions for 1979, and that the priority would be for relief to residential property owners.

Council member Marion Barry (D-at large) chairman of the Council's finance and revenue committee, said he also is seeking "substantial relief" for city homeowners, beyond the $6,000 property tax exemption and tax relief for the elderly, blind disabled that the City Council passed this year.

But Tucker's proposal to begin the budget process with an across-the-board cut, with the approval of Barry, drew an assocation by Council members John A. Wilson (D-Two) that the proposal was "politically motivated," and that the proposal was "arbitrary."

In the past, the top Council members in the budget review process, the chairman of the finance and revenue committee that determines how much the city will have to spend, and the chairman of the budget committee that determines how that money should be spent, have been sharply divided over the budget.

Last year, the Council abolished the budget committee and gave reponsibility for how the city's money should be spent to the entire Council.

This year, the argument to determine how much the city should raise in revenue and how that money should be spent could be intensified because Barry, chairman of the finance and revenue committee and Tucker, chairman of the Council, are likely to be political rivals in the 1978 mayoral election.

Both are seeking to reduce the budget offered last week by the Mayor Washington, who according to those close to him, is still studying whether to run for re-election.