Negotiators representing 6,000 District of Columbia public school teachers reached tentative agreement yesterday with the city's school board on a three-year contract that sources said would give the teachers a 21 percent pay increase over the duration of the contract.

City officials also announced yesterday that they had reached a three-year agreement on working conditions with 10 locals representing about 6,000 workers in more than half a dozen city departments and agencies. Pay increase agreements had already been reached with those groups.

The teacher pact, which will be submitted to union members for ratification within three weeks, would grant the Washington Teachers Union increased authority to protest annual job performance ratings given by principals and the right to collect union dues from the estimated 1,800 teachers who are not members of the union, according to sources on both sides. The latter provision could produce more than $70,000 a year in additional funds for the union.

In return, the sources said, the union agreed that teachers would start work 15 minutes earlier, end work 15 minutes later and also work four more days each year. The teachers' refusal to accept similar extended day and extended school year provisions contributed to the 23-day teacher strike in 1979.

The union also compromised on a hard-fought school board proposal that would require them to achieve a better-than-satisfactory rating after five years in the system in order to receive scheduled pay increases in the sixth year, according to the sources.

Both school board and union representatives, who declined to publicly discuss details of the proposal, said yesterday that the tentative contract gives wide gains to each side.

"It is an agreement that will suit the needs of both parties and serve the school system well," said union president William H. Simons. He said he will send copies of the preliminary agreement to his membership next week. The union will discuss the contract at a March 22 meeting and ratification is expected by March 30, Simons said.

Stephanie Cabaniss, a negotiator for the school board, said, "We are very pleased we have been able to reach a mediated settlement. We believe this agreement will provide a basis for effective school operations which will result in improved education for public school students."

The provisions agreed on yesterday would extend the teachers' work day from 6 1/2 hours to 7 hours, excluding a half-hour lunch period. This would mean teachers would be expected to arrive at work no later than 8:30 a.m. instead of 8:45 a.m. and leave at 3:30 p.m. instead of 3:15 p.m.

The contract would also require them to work 210 instead of 206 days a year. Neither provision would change the length of the children's school day or school year.

School system officials had been anxious to win extended day and extended year provisions to increase the amount of time that teachers would be available to do administrative work, prepare for classes and meet with parents.

Under the contract, the teachers would receive a 6 percent pay increase for this year, 7 percent in fiscal 1983 and 8 percent the following year. That is 1 percent less than the city police officers and firefighters have negotiated, but more than the school system's other employes have won so far. The average city teacher now earns $25,000 a year.

The proposed contract also contains language that allows the teachers to protest the job performance ratings they receive from the principals who supervise them, even if they receive a "satisfactory" or "very good" rating. Current policy is that only those who have received an "unsatisfactory" rating can protest their evaluation.

The outstanding ratings are especially coveted during times such as these when employe layoffs are a constant threat. When a reduction in force takes place, teachers with the least seniority are the first to go, but those rated outstanding get four extra years of seniority added to their service record.

But for the first time, teachers would be required to receive a better-than-satisfactory rating in order to receive their pay increase when they are entering their sixth year on the job, and moving from a salary of $16,800 to $17,506. Currently, teachers need only a satisfactory rating to receive their pay increases.

That stipulation is not expected to go into effect until the last year of the contract, 1984, according to sources on both sides. A union source said that because of recent layoffs, most teachers now in the system have 10 or more years of service and the better-than-satisfactory requirement will affect only a small number of teachers who will have less than six years experience by 1984.

James Ricks, who challenged Simons unsuccessfully for the union presidency last year, said he intends to urge members to reject the proposed contract because Simons "failed to negotiate any job security for teachers."

The contract agreement with American Federation of State, County and Municipal Employees locals that was announced yesterday by Mayor Marion Barry follows a wage agreement reached in January. Salary increases and bonuses, retroactive to Nov. 1, had been held up until the issues over working conditions had been settled.

If the AFSCME workers ratify the contract next week as expected, the higher wages will go into effect March 16, city officials said.

Under the working agreement, the city obtained greater flexibility in contracting for services that in the past have been performed by unionized city employes.

The union locals won the right to collect service fees from nonunion members covered by the bargaining contract as long 60 percent of the employes in each of the locals are dues-paying members of AFSCME.

City agencies affected include the departments of Environmental Services, Human Services, General Services, D.C. General Hospital, Office of Finance and Revenue, Financial Management and the Department of Licenses, Investigations and Inspections.