The Washington school strike worsened yesterday as teachers' representatives said they would not accept an interim agreement, other unions threatend to join the strike, and Mayor Marion Barry proposed no new efforts to bring the teachers and the school board together.

School Superintendent Vincent E. Reed said the school cafeteria workers and the janitors' unions join the illegal teachers' strike tomorrow morning. The strike began its fourth week today.

Reed said he is asking parents to send their children to school with lunch bags beginning tomorrow if school lunches are not availavle.

"We can't close schools because of the court order," said Minnie S. Woodson, the school board president. She was referring to a weekend order by D. C. Superior Court Judge Gladys Kessler that teachrs return to classes by yesterday.

"The court order said teachers were to return to the classroom this week," Oodson said, "and by implication that means there have to be open classrooms for them to return to."

Robert P. Bates, an organizer for the American Federation of Teachers, said he saw no reason for the teachers to return to work without a permanent contract.

"They would be right back where they started from except they would be in school instead of out," said Bates, who has been a consultant to the striking Washington teachers' group. "If they have that much difficulty negotiating when they are on strike, what makes you think they can bargain when they are in?"

Bates said he thinks the schools should be shut down. "It's a cruel hoax on the community to try to convey the idea that there is education taking place," he said.

Meanwhile, two union locals representing 4,000 cafeteria workers, teachers' aides, clerks, engineers and janitors in the city's 200 schools said they are prepared to join the teachers' strike tomorrow morning.

Geraldine Boykin. Xecutive director of District Council 20 of the American Federation of State, County and Municipal Employees, said the AFSCME locals would join the teachers to bring added pressure on the school board.

"We are parents, too," Boykin said. "We care about our children..."

Mayor Maion Barry, who on Sunday abandoned his plans either to bring the two parties together personally or to negotiate his won strike-ending agreement with the teachers' unvery much in the picture."

Barry would not say immediately what he plans to do. Sast night, as he emerged from a meeting on toher business, the mayor said, "I don't have a solution yet" to the teachers' strike.

Florence Tate, the mayor's press secretary, said Barry had net for four hours with key aides to discuss "the next steps that he can take to try to bring a settement to the strike or have the teachers go back to work. He has some next steps, but he's not ready to say what they are."

On Friday, Barry had threatened to supersede the school board and negotiate his own agreement with the union if the two sides did not reach an agreement over the weekend. Barry convened round-the-clook negotiations at the Hotel Washington Friday night in a self-described "last ditch" effort to end the strike by Monday.

Little progress was made in the talks, which ended after Kessler's latest back-to-work order was handed down Saturday morning. After the union announced that it would not obey the order, Barry, saying he was "disappointed," withdrew his request that the City Council give him special emergency powers to negotiate a pact to end the strike. Barry said he would no longer try to bring the two sides together.

School board President Woodson said that the board sent a letter to teachers yesterday and ran a letter to teachers yesterday and ran a newspaper advertisement in The Washington Star to combat "things the union is telling the teachers that just aren't true." Woodson said the central message in both the ad an the letter was that there will be no reprisals by the school systems against striking teachers who decide to return to the classroom if they have not harassed persons or committed violence while on strike.

"This strike cannot continue forever," Woodson said. The superintendent has the authority to fire people and if his school system cannot run properly then he will have to do something. There is no timetable set for firings but it can't linger on much longer."

Negotiations between the union and the board's negotiators began at 10:30 a.m. yesterday and broke off late last night with no progrees reported. Anothr bargaining session has been scheduled for today. James R. Williams, a mediator with the Federal Mediation and Conciliation Service, said that the union and the board did not meet face to face yesterday.

"At this point there has been no progress, no change in either side's position," Williams said.

Williams said mediators are still seeking to achieve an interim agreement between the board and the union although the union has said that it now will not end the strike unless a complete agreement is reached on a new contract.

Boykin said the AFSCME locals voted Sunday to support the teachers' strike because "their fight is our fight..."

Yesterday morning Ouncil 20 sent fliers to all its members who work in the city schools tlling them: "All members of our unions will observe the picket lines of the teachers' union at all school sites."

The school board, which brought the lawsuit that led to the Judge Kessler's back-to-work orders, must initiate any new court action in response to the union's failure to obey the judge's lastest order. No such subsequent action was begun by he board yesterday.

A hearing was tentatively scheduled for this afternoon before Judge Kessler on a request by the board to require that the union begin paying the hundreds of thousnds of dollars in fines resulting from its failure to obey a March 12 back-to-work order.

That order lastd through Friday. By that time the union unofficially owed $503,250 for violating the order for 11 days. Union lawyers do not include weekend days in their calculation of the fine, thus reducing their unofficial esimate of money owed to $343,350.

It also was unclear yesterday whether the fines would continue to mount even though the March 12 back-to-work order has been replaced with a new order as of Saturday.

If the fine escalation does continue, the union would; by its own formula owe $503,250 through today. The amount would be $914,520 and increasing by more than $100,000 each day if weekend days are included.

It is up to Kessler to determine how the fines will be calculated.

School officials said yesterday that about half the city's 6,000 teachers and about half the school system's 113,000 students attended classes yesterday, the same proportion as throughout most of last week.

School officials also announced yesterday that they have established a telephone hotline, in English and Spanish, to give parents and teachers the latest information about the strike. The number is 727-9108 for the English version and 727-9110 for the Spanish.