The operating budget for the D.C. public schools would be increased by nearly 6 percent in the coming year, to a total of $359.5 million, as part of Mayor Marion Barry's fiscal 1986 budget proposal that will be submitted to the D.C. City Council today.

For the second year in a row, Barry and members of the D.C. Board of Education have agreed on an acceptable spending level for the schools, the mayor's office announced yesterday. In previous years, the mayor and the school board waged bitter battles over spending, with the City Council serving as the ultimate arbiter.

The proposed 1986 school operating budget would represent an $18.8 million increase over the current spending level and a $32 million increase over the 1984 level.

Barry also will ask the council to approve $22.5 million in capital borrowing for the schools in the coming year, to cover the cost of removing asbestos from buildings and to make other improvements.

"While this mark is not all that the school system had wished, it represents an affordable and positive level to continue progress for our young people," Barry said in a statement released by his office.

The mayor's 1986 budget request will be about $9.1 million less than the school board originally sought. Board of Education President R. David Hall said yesterday that the spending level finally agreed to, after weeks of negotiations, would cover mandatory increases in personnel costs and a "modest" expansion of school programs.

Hall indicated that the school board intends to lobby the City Council for additional funds, despite the agreement with Barry.

"We have gone as far as we can with the mayor and we are pleased the mayor has come along this far," Hall said. "We are hopeful that we can get some additional funds to expand programs a little more."