City Administrator Elijah B. Rogers notified Washington school officials yesterday that they are free to begin hiring 275 new teachers despite a congressional dispute that has delayed passage of the fiscal 1983 D.C. budget.

That budget includes a $42 million increase to pay for new teachers in the fiscal year that began Oct. 1. When the budget failed to pass before a six-week congressional recess began last Friday, school officials said they would have to delay the planned hirings.

Yesterday, however, School Superintendent Floretta McKenzie received a memo from Rogers saying that while D.C. government agencies must hold their spending to fiscal 1982 levels until the new budget passes, the school system is exempt from that requirement.

School system legislation officer Clarence Daniels and city Budget Director Gladys Mack said the exemption was possible because neither the Senate nor the House appropriations committee disagreed with the Board of Education's request for a $306.5 million budget in fiscal 1983.

"We are ecstatic," McKenzie said yesterday. "In order to get the full benefit of this expanded budget we needed the funding for the majority of the school year. This action will enable us to have a direct and immediate impact on improving instruction."

Hiring the new teachers will reduce student-teacher ratios from 28 to 1 in elementary schools to 25 to 1 and from 28 to 1 in high schools to 26 to 1.

Student-teacher ratios in industrial arts classes will be lowered even more by additional teachers, to 20 to 1 from a current level of 28 to 1, said school system spokeswoman Janis Cromer. The new budget also will allow the system to hire clerical aides to help each teacher with noninstructional work, provides $1.1 million for new computer equipment and $912,000 for new buses for handicapped students.

"We would have had to wait possibly until mid-Decmber to do this if we had not been exempted," said Associate Superintendent Arthur G. Hawkins.

The fiscal 1982 school budget was $264.3 million. Passage of the city's new budget, including the increased school funds, was delayed by a dispute over proposed restrictions on the use of the new Washington convention center.