Negotiations between the Washington School Board and the city teachers' union broke off in bitterness yesterday as the union substantially increased its demands for the first time in the almost two-week-old strike.

"The time has come to escalate our demands," union president William Simons announced at a rally after he presented the new union proposal, which seeks substantial salary and benefit increases in 1980, when the board gains authority to set teachers' pay.

"Now we can tell those (teachers) who are not participating (in the strike) that there is something in the pot if you care to participate," Simons said.

The school board's chief negotiator, Kenneth W. Nickoles, characterized the union's new demands as "quite a laundry list." He said the board rejected them as "totally unacceptable" because the board does not have the legal authority to negotiate them now and cannot commit itself so far in the future. Teachers' salaries now are set by the mayor and City Council and are reviewed by Congress.

No new negotiations were scheduled after yesterday's 90-minute session ended.

Simons urged the strikers to "redouble our efforts" at picket lines this morning.

School Superintendent Vincent Reed said schools would remain open, as they have every day since the strike began March 6.

After a meeting with top aides at the District Building last evening, Mayor Marion Barry criticized both sides in the dispute for their "cavalier attitude" and appealed for new efforts to end the strike. Barry said he would phone federal mediators to try to arrange a new negotiating session for 10 a.m. today, but as of midnight mediators said they had not heard from the mayor.

The mayor also disclosed that on Thursday he had sent a new proposal for an interim agreement to end the walkout to school board President Minnie S. Woodson but had not yet received a reply. The new proposal, however, appeared to be similar in most respects to a Barry compromise plan spurned by the board last week.

Until yesterday, the contract talks had centered on nonmoney issues, such as work rules and the relative authority of the school board and the union.

Since last Wednesday, when the board offered to sign an interim agreement, both sides appeared to be trying to narrow the issues in an effort to arrange for teachers to return today to their classrooms.

After yesterday's new union proposal, Nickoles said the effort now seemed "fruitless."

"It takes two to tango," Nickoles said, "and if one side doesn't want to, I can't sign a contract with the mediator."

Simons declared, "We tried to be reasonable, but all our reasonableness has been to no avail... We have tried to come all the way down to minimum demands, but now the time has come to escalate...."

"This (school) year is almost over," Simons added. "Now we're looking ahead."

The Greater Washington Central Labor Council announced yesterday that it will sponsor a demonstration Tuesday at school administration headquarters and the District Building in support of the striking teachers. The council said the demonstration would be conducted by members of all labor unions in the city.

Unionized school custodians, secretaries and cafeteria workers have continued to cross the teachers' picket lines since the strike began.

When one teacher at yesterday's rally shouted, "We need more than sympathy," Arline Neal, the first vice president of the Labor Council, said other unions have been deterred from joining the strike by their own contracts with the school board.

"There are certain legal angles," she said.

Under the union's new proposal, its old contract, which the board has sought to change as too pro-union, would be extended until Aug. 31. In addition, the board would have to promise "no reprisals" against striking teachers, including an end to its lawsuit in Superior Court that already has resulted in a contempt order against union officials.

As of today, fines for violating Judge Gladys Kessler's no-strike order total $114,750.

For the next year -- from Sept. 1, 1979, to Aug. 31, 1980 -- the union asks for the following:

A 10 percent salary increase.

Cost-of-living raises four times a year based on changes in the Consumer Price Index.

Shortening the time it takes for teachers to reach top salaries from 15 years experience to 6 1/2 years. The maximum salaries now range from $20,852 for the nine-month school year for teachers with a bachelor's degree to $25,789 for those with a doctorate.

Free medical, dental, and optical insurance.

Full reimbursement for all courses taken to meet board recertification requirements.

A promise that the board will buy textbooks and supplies with money recovered from the city government because of a successful lawsuit against job-freezes by former Mayor Walter Washington.

In addition, the union asked that all teachers who have lost pay because of the strike be allowed to make up the time by working additional days in the spring.

"We want to make sure that students get a full year of instruction," Simons said at yesterday's rally. But he added that, under the union proposal, "those teachers who lost pay (by striking) will be the only ones eligible (for the extra work in the spring)," suggesting that those who have continued to work despite the strike not be able to earn anything extra.

School and union officials have given widely differing estimates of the number of teachers participating in the walkout. The union has stated that about 80 percent of the city's more than 6,000 teachers have stayed off their jobs. School officials said that nearly half of the teachers were at work last week.

School superintendent Vincent Reed has acknowledged that the strike has had a "devastating" effect on school programs, with student attendance down to about 50 percent. Reed said he expects the school system to hold summer classes for makeup and advanced work for the first time in two years. He said no plans are being considered to extend regular classes beyond the scheduled last day of school on June 14.

At the rally, which drew about 800 teachers to the Metropolitan AME Church on M Street NW, Simons urged the board to drop its present team of negotiators, which is made up entirely of school administration officials.

"We ask that they bring to the table each member of the Board of Education, the Mayor, and the City Council," Simons said. "Get to the table those people who can respond so we can get this dispute settled."

In an interview last night, board president Woodson said she had confidence in the school system's negotiators and thought it unwise for board members to take part in the talks themselves.

"I don't feel negotiations can be done well by novices," Woodson said, "and we (board members) are definitely novices... For union leaders (labor contracts) are their entire business and they're extremely shrewd and good at it."

Woodson said she thought Mayor Barry's new proposal contained only small changes from the interim plan he presented originally. The board had spurned that proposal, she said, in favor of its own compromise plan.

After meeting with his top advisers for about two hours last night, Barry told a press conference that the teachers strike was harming the city and not just the schools.

The mayor said juvenile crime had increased substantially, with a 12 per cent rise in juvenile "contacts" with police since the strike began. Groups of youths now are roaming the streets, Barry said, instead of attending school.

Because of numerous bomb threats to schools, Barry said the police bomb squad is overworked. Welfare officials at the meeting said poor families had been hurt because in many cases children receiving free lunch and breakfast in school cafeterias were staying home.

"We're going to pull out all the stops," Barry said. "I'm not trying to negotiate for the board or the union, but to end the strike."

Simons said late last night that Barry had last talked to him on Friday, and never mentioned his modified proposal for agreement.

"The strike is still on," Simons declared.