D.C. City Council Chairman David A. Clarke said yesterday he might support the school board's efforts to increase Mayor Marion Barry's budget for the public schools next year, but only to provide money that might be needed to avoid teacher layoffs.

Clarke's comments followed a noisy, daylong City Council hearing on the mayor's proposed $318.5 million operating budget for the schools for the coming year--an increase of $12 million over current spending, but $18 million less than the schools requested.

"My goal . . . is to avoid RIFs of teaching personnel . . . This process is more attuned to drama than to accurate budget analysis," Clarke said after the hearing, which was attended by several hundred educators, parents and teachers in the council chambers on the fifth floor of the District Building.

Clarke, who has been critical of the schools' spending practices, did not indicate how much of an increase in Barry's proposal he would be willing to support.

School board President David Eaton, who attended yesterday's hearing, has talked privately with Barry and Clarke about compromising at $330 million, according to several sources.

But yesterday, Eaton stuck to the public position that Barry's proposal is too little to maintain school services and that 400 teachers may have to be laid off. "These are drastic and unacceptable reductions," Eaton said.

In a related issue of school-system finances, Eaton also insisted yesterday that city officials had failed to warn the school system early enough that it would have to get along this year with $7 million less than budgeted.

Eaton and School Superintendent Floretta D. McKenzie, who said they would have to cut services to make up for the loss, contended they were formally told of the reduction only last week. The mayor and council officials said the schools have known informally about the cut since last October.

The school officials received a friendly welcome from some council members, including Hilda Mason (Statehood-At large), chairman of the education committee and a strong supporter of city schools.

But Clarke's questions were pointed. He grilled school officials about why they had RIFed 56 employes while underspending their personnel budget by $7.6 million, and also asked why, in a period of declining enrollment, the schools were increasing administrative staffs and eliminating 122 teacher positions.

Before schools officials could fully answer Clarke's questions, Eaton interjected, "My administration has a right to reflect on these detailed questions." He promised to supply the answers in writing later.

Elizabeth Reveal, Barry's budget director, later raised the same points in her testimony that Clarke had made, calling the school board's request for 1984 "both unnecessary and excessive."

McKenzie, who was given a standing ovation for several minutes in the crowded chamber, said cutting back on education would affect the whole city. "When a tree growing in a park or back yard is thriving and blossoming each year, you don't pull it up to inspect the roots and check out how it's doing. The same is true for schools." CAPTION: Picture, Teachers, parents and school officials throng the D.C. Council chamber for the hearing yesterday on the mayor's proposed $318.5 million operating budget for the schools. By James K.W. Atherton--The Washington Post