Negotiators for the Washington Teachers' Union and the city school board reached tentative agreement last night on a new two-year contract, ending the possibility of a strike when teachers are scheduled to report for work on Tuesday.

Kenneth Nickoles, the school board's chief negotiator, said the new pact was based largely on recommendations made in early August by a fact-finder appointed after a bitter 23-day teachers' strike in March.

"There was a little give and take on both sides," Nickoles added. But he refused to spell out what changes were made from the report issued by James M. Harkless, the fact-finder.

Teachers' union president William Simons announced the agreement in a tape-recorded message to his members over a telephone "hot line" that the union maintains.

"Everyone can relax now and have a joyous weekend," Simons declared in the recording, "a very joyous Labor Day weekend."

He could not be reached by reporters for further comment. But Simmons' assistant, Harold Fisher, said the union's 20-member executive committee would probably meet Tuesday night to consider the pact. Fisher indicated that a ratification vote by the union's 5,000 members probably would take place within two weeks after copies of the pact are distributed.

School board president Minnie S. Wood said the 11-member board would hold its ratification vote only after the union ratifies the pact. Woodson noted that the board already had voted unanimously to accept Harkless' recommendations. She said she thought the union and the board would ratify the proposed contract.

When Nickoles phoned her about the tentative agreement, "I felt utter joy," Woodson remarked, "because fall classes (scheduled to being Sept. 10) will be able to start smoothly."

I think it's a good contract for both sides," Nickoles said. "Now I'm going home and spend some time with my wife. We've been negotiating almost every day for the last two weeks."

Yesterday's five-hour session involved only Simons and Nickoles, sitting across a small round table in Nickoles' office at school board headquarters.

Despite union requests, Nickoles said the new contract included no promises that the school board will support a reduction of the $343,000 fine imposed on the union by D.C. Superior Court Judge Gladys Kessler for violating a no-strike injunction.

However, board members indicated previously that they would make no objection to the union request that the fine be pared to $65,000.

Nickoles indicated that the board and the union agreed that no disciplinary action would be taken against teachers just for taking part in the March strike, but that the board could take action against strikers for alleged acts of vandalism and initmidation, provided charges were filed by Sept. 15.

The school board and the union have been feuding over the teachers' contract since January 1978 when an 18-month pact expired.

The board contended that agreement gave too much power to the union and required teachers to spend too little times in the classroom.The union countered that the board was trying to "break" the union and take away gains teachers previously had won.

The strike in March left most of these issues unresolved. It was brought to an end after intervention by Mayor Marion Barry when Judge Kessler met a key union demand and extended the old contract until mid-summer.

In his report, fact-finder Harkless recommended that the union accept board proposals dealing with teacher evaluations, student grading, hall duty and record keeping.

But on the major issues that prompted the confrontation -- extending the school day, lenghthening the school year and restricting grievances that could go to arbitration -- Harkless sides with the union, leaving past practices unchanged.

When the negotiations resumed Aug. 20, Simons presented a list of 35 changes in Harkless' proposed contract language, but by yesterday, sources said, differences had been narrowed to about five points.

Agreement was clinched, sources said, when the board accepted a union proposal that teachers be allowed to file grievances, leading to binding arbitration, on "conditional" ratings, instead of only on "unsatisfactory" ratings, as Harkless provided.

In return, the union agreed to increase the number of parent-teacher conferences from three nights a year to four.

Throughout the protracted struggle, money was never an issue between the two sides because Washington's teacher salaries -- the highest in the area -- are set by the mayor and City Council, not the school board. The next raises, due Oct. 1, are tied to those granted federal workers, which President Carter set yesterday at 7 percent.

As part of the tentative agreement, negotiations on salaries, hours and the length of the school year may begin at the request of either side after Jan. 1 when the board is to gain the power to negotiate salaries under the new city personnel law.

Unless both sides agree to changes, however, the contract provisions would remain in force until Sept. 1, 1981.