Members of the Washington School Board asserted last night that Mayor Marion Barry had asked them to make such sharp cuts in school spending next year that class size would balloon and more than 400 teachers would have to be fired to meet Barry's demands.

Angrily responding to a directive from the mayor's budget office which Barry underlined at a meeting with board leaders last week, school board member John Warren declared:

"This mayor calls himself a friend of education. If he calls what's taking place now friendship, it would be better if he went around setting fires to all the school buildings in this city."

School board president Minnie S. Woodson said that at the meeting Barry suggested that the board close 20 more schools because of declining enrollment as a way of bringing school spending down to $241.3 million in the 1981 fiscal year.

"There's no way we could do that," Woodson said she replied, "without hurting children and hurting communities, and we'd save only a small part of the money he wants."

Board members also complained that the mayor's low budget ceiling also would tie their hands in any future negotiations with the Washington Teachers Union, in which the board hopes to tie pay raises with lengthening the school day and the school year.

Yesterday, representatives of both the board and union reported progress in the third straight day of negotiations since contract talks resumed on Monday.

The school board voted unanimously on Aug. 13 to accept virtually all the recommendations by fact-finder James M. Harkless. The union responded more coolly, suggesting 35 changes in Harless's proposed contract language.

The union also sought board support for reducing a $343,000 fine imposed on it by a D.C. Superior Court judge for violating a no-strike injunction.

Instead of the fine, union president William Simons proposed that the union contribute $65,000 to a scholarship fund.

Board members said they would not join in asking Judge Gladys Kessler to reduce the fine, but most said they would not oppose any union effort to do so.

Sources for both sides said they thought the issue of fines would not stymie a settlement. Talks will resume this morning at 10 a.m.

Under the new city personnel law, the school board will have the right beginning Jan. 1 to negotiate salaries, which now are set by the mayor and City Council.

The board suggested that its new contract with the teachers run for three years and that either side have the right to reopen negotiations on wages and work time as soon as the new personnel law takes effect.

The union suggested that the contract last two years and that any earlier talks be confined to wages and benefits.

In discussing the budget last night, school board member Frank Shaffer-Corona described Mayor Barry as "the friend of the Washington Teachers Union," but then added: "He's setting up conditions under which hundreds of his friends will have to look for other jobs next year. With friends like that, who needs enemies?"

The budget memo sent to the school board Aug. 7 by assistant city administrator Gladys Mack, said the mayor had set his "planning mark" for the 1981 school budget by taking into account an expected 6,200 drop in student enrollment. She said this would permit spending to be cut by about $10 million, compared to what the board expects to receive from Congress for the 1980 fiscal year, which starts Oct. 1.

Mack said the board could make the cuts without increasing pupil-teacher ratios if it closed some schools, used energy-saving devices, and moved to curtail nonpersonnel costs.

But Deputy School Superintendent Edward Winner told the board last night that the mayor's budget figure was based on faulty arithmetic.

Rimming the teaching staff to keep pace with enrollment declines would require a cut of 705 teaching jobs, out of about 6,400, over the next two years, Winner said. It probably could be achieved, he said, through normal retirements and resignations.

But Barry's budget figure is so low, he said, that it would require an additional 423 teachers to be cut in 1981, which could only be done by firing almost all of them. Such a cut-back, he added, would increase average class size from 26 pupils to 28.

Last month the board said it wanted $295 million for the 1981 fiscal year with no cuts in staff. Yesterday, the members spurned a suggestion by Supt. Vincent Reed that the budget be trimmed to $250 million, and they would hold public hearings before deciding what figure to recommend.

Yesterday's strong attacks by school board members on Barry followed the mayor's comment in a speech Saturday that the board had been "a little chicken" in bowing to public pressure not to close schools that were underenrolled. He also complained that the size of the school administration was too large and had been "creeping up" since Barry himself had headed the board in the early 1970s.