The Washington Board of Education presented a new back-to-work proposal to the city teachers' union yesterday as negotiations to end the teachers' two-week-old strike resumed with an all-day bargaining session.

When the talks ended at 9:30 p.7., federal mediator James R. Williams reported that there had been "no movement in terms of official positions, but we're still exploring a number of possibilities."

Williams said the talks would resume this morning.

Yesterday's negotiations, which began at 10 a.m., were the longest since the crippling strike began March 6. On Sunday the talks broke off after just 90 minutes when the union made major new demands for salary and benefit increases.

Williams said the board proposal for an interim agreement to get teachers back into their classrooms was "the basis for all discussion yesterday." Sources indicated that the union had not pressed its "escalated" demands that the board had rejected on Sunday.

"I think both sides are interested in finding a basis for an agreement," Williams said, "but they still have major differences... I can't report anything of a positive nature, but I don't want to be overly pessimistic either. These things take time."

Williams said that for most of yesterday the mediators met separately with the two sides, but that joint sessions were held for about an hour. The talks took place at the headquarters of the Federal Mediation and Conciliation Service on K Street NW.

As he left for the night, school board chief negotiator Kenneth W. Nickoles said the union had neither accepted nor rejected the board's proposal or offered a counterproposal of its own.

"I was quite hopeful when I came here this morning, and I am still hopeful," Nickoles remarked. "We explored numerous areas of possibility."

Throughout the day, union President William Simons remained noncommittal about the board's new proposal. "We're looking at it, we're looking at it," Simons said during one break in the talks, and waved reporters away.

Under the board's new proposal, which is patterned on a recent recommendation by Mayor Marion Barry, teachers would go back to work immediately in return for reinstatement of several key provisions of the union's former contract. These include sections dealing with grievances, teacher discipline, involuntary transfers, and limitations on nonteaching duties.

The plan stipulates that after the teachers return to work, the two sides would engage in four days of around-the-clock negotiations in an attempt to settle long-term contract issues. Unresolved issues remaining would then be submitted to a fact-finding panel for further recommendations.

According to members of the school board, its new proposal promises that no reprisals will be taken against teachers for participating in the strike, but that disciplinary action may be taken against strikers for violence or harassment during the walk-out.

The proposal also would not restore the union's dues checkoff, which yielded more than $70,000 a month in dues, or other contract provisions dealing with grades, student discipline, and claimed is excessive and has sought to curtail.

As the negotiations continued, about a thousand persons, including striking teachers and officials of labor unions supporting the teachers, marched around the scool board building and the District Building yesterday.

The marchers then held a noontime rally on the steps of the District Building with labor union leaders shouting statements of support for the teachers.

Douglas Moore, former City Council member at large, marched with the teachers. "I have 17 teachers and two principals in my family," Moore said. "Teachers are nothing but second-rate citizens in our society. This society lies when it says teachers are great and then gives them low pay and no responsibility. We lie."

At the labor rally, several union leaders, including teachers' union officials from Ohio and Wisconsin, told the marchers that the teachers' strike was a "labor union struggle." Officials of unions represening firemen, policemen, postal workers, public employes, transit workers and other unions spoke to the strikers, promising that members of their union would join picket lines.

William Lucy, chairman of the American Federation of State County and Municipal Employees, pledged $1,000 to the teachers' union.

After the rally a delegation of union officials met with the mayor. Union President Simons briefly joined the meeting during a break in negotiations, but he did not stay unitl the end of the meeting.

"I just went in to see how things were going," Simons said as he waited for an elevator outside the mayor's office. "I didn't ask for this meeting with the mayor."

After meeting with the 12 labor union officials, including representatives from the American Federation of Teachers and the American Federation of State County and Municipal Employes, Barry said he felt that yesterday's daylong negotiations between the board and the union were a "breakthrough."

"... I made my position clear to them," the mayor said. "I told them I'm not taking sides with the board or the union. I'm interested in getting this strike over with. This strike is illegal and I told them that."

Barry said he has several proposals for getting teachers back to their classrooms but he would not say what those plans are.

Meanwhile, at school board headquarters yesterday afternoon, Frank Shaffer-Corona, an at-large member of the board, called D.C. police seeking the arrest of R. Calvin Lockridge, the school board member from Ward 8 who is a member of a rival faction on the board.

Shaffer-Corona accused Lockridge of squeezing his neck Monday night during a closed board meeting, saying that Lockridge had to be restrained by Superintendent Vincent E. Reed.

Lockridge denied Shaffer-Corona's accusation. No charges were placed against Lockridge and he was not arrested.

"You know how Shaffer is," Lockridge said in front of school board headquarters. "He's always calling people clowns who don't agree with him..."

In another development, William Peer, a lawyer for the teachers' union, told D.C. Superior Court Judge Gladys Kessler yesterday, "The public interest does not demand that the schools stay open. If that were the case, the school board would have settled this strike long ago."

Peer made the argument at a hearing on the school board's bid to secure a preliminary injunction against the strike. The union lawyer said he has "been waiting for evidence (from the school board) that a vital public service is being affected" by the strike.

But Deputy Corporation Counsel John A. Earnest told the judge that the union is continuing the strike "in total contempt of your order. To say the public interest doesn't cry out in this case belies reason."

Kessler continued her temporary restraining order against the strike through 6:15 tonight, although Peer said the union believes that the restraining order expired last Thursday, 10 days after it was issued. The judge tentatively scheduled another hearing on the school board's bid for the injunction this afternoon.

School administrators reported that 47 percent of the city's more than 6,000 teachers were in their classrooms yesterday -- about the same figure as was estimated for the past week. An administration spokesman said that about 51 percent of the city's 113,000 students were present slightly more than the attandance reported late last week.