For the first time in the four-year history of home rule, the D.C. City Council voted yesterday to increase instead of cut the city's proposed operating budget, adding $10.9 million to the total proposed by Mayor Walter E. Washington.

More than half the added money, $6 million, would go for schools. Top school officials, while pleased, said the total falls short of the $16.2 million extra that is needed for the 1980 fiscal year, which begins Oct. 1, 1979.

The action was taken by the full council sitting as a budget committee and was preliminary. It must be reaffirmed by two future council votes. Congress will have the final word.

Mayor Washington had proposed a school budget of $258 million an increase of $5 million above the current 1979 fiscal year.

The school board asked the council for another $16.2 million, pushing the total incrase to more tha $29 million. The board contended that about half the increase in needed to pay mandatory costs, such as within-grade pay raises and higher utility expenses, and half to provide improved services such as reopening summer schools and providing pre-kindergartens.

Betty Ann Kane, school board finance chairman and the Democratic nominee for an at-large council seat, said she would continue to push for the full budget.

"I think the council action shows that we are starting to get the message through that education must beadequately supported." Kane said, but "I don't concede that (the voted increase) is adequate, given inflation and the increasing requirements for the school system, especially laws and court orders requiring special education for the handicapped."

Conrad P. Smith, school board president, said the board may have to consider cuts in educational services.

In taking its action, the council adopted language urging the school board to give priority to spending on books, supplies and equipment over hiring new personnel. Three council members voted against the directive - Hilda Mason (Statehood-At Large) and WIlhemina Rolark (D-Ward 8).

By law, the proposed budget submitted to Congress must be balanced, with estimated income at least equaling outgo. To vote a higher spending figure yesterday, the council would have to raise taxes, which it decided in advance that it did not want to do.

Yesterday's increases were made possible by a new and higher tally of what the city collected in local taxes in the 1978 fiscal year that ended three weeks ago. The city collected $10.4 million more than it had expected, and that money could be carried forwaRd to help fiance a large 1980 budget.

The revised budget, totaling $1.411 billion, was recommended by Council Chairman Sterling TUcker. The mayor has the right to veto individual items, but an aide said he probably would support the higher school spending.

Tucker called for the $6 million additional for the schools as a compromise. The council's education committee, headed by William R. Spaulding (D-Ward 5), had supported the entire amount sought by the school board.

In addition to the school increase, the council added $2.5 million to begin a $15 a-month local supplement to social security income for some elderly and permanently handicapped people, $1.3 million to begin rent supplements under the rent control law and agreed to the full authorized funding of $1.1 million for the city's 36 advisory neighborhood commissions.