The Washington school system sent layoff notices yesterday to 67 teachers, including 37 whom it tried to fire last fall. All 37 were reinstated by the U.S. Civil Service Commission.

Officials said the cutbacks were necessary to keep within the school budget, which provides for 114 fewer teachers than a year ago.

But leaders of the Washington Teachers Union suggested that administrators be fired, too, as school employment shrinks because of a loss of students.

Officials said that because of the enrollment decline, average class size this year will be unchanged from a year ago.

Personnel director Claudette Helms said 30 of the teachers being laid off work in junior and senior high schools. Included are 12 business teachers, eight in physical education, five in foreign languages, three in home economics and two in music.

Because the school has done almost no hiring for several years, Helms said most of the laid-off teachers have more than five years of services and some have been working for as long as 10 years. The system employed about 6,900 teachers last year.

All the layoffs are carried out according to seniority.

Helms said cutbacks were made in particular areas not just because of the general enrollment decline but also because students were choosing some subjects less frequently as electives.

The other 37 teachers who have been notified that they will lose their jobs at the end of August are special-subject teachers in elementary schools, most of whom teach foreign languages and music.

The elementary teachers originally were told they would lose their jobs last September as part of a group of 70 who were laid off then. But they won reinstatement from the Civil Service Commission, which still governs D.C. personnel actions, because improper procedures were followed.

Yesterday Helms said, "We're in the same financial bind as we were last fall, so we have to (lay them off) again. We still do not have the money for those operations."

Harold Fisher, assistant to the president of the Washington Teachers' Union, said the union would fight all the layoffs, and added:

"If teachers have to be reduced, then surely you don't need the same number of administrators to run the system. We think it's time that teachers stop being the only ones who are sacrified."

According to the school budget office, the number of administrative positions has dropped from 500 to about 470 over the past year two years. All the reduction was achieved without layoffs through retirements and resignations.

In May, the D.C. school system sent layoff notices to 105 elementary classroom teachers, but Helms said 40 of them now have their jobs back because other teachers have quit or retired.

She said she expected very few of the new group getting layoffs notices would win a similar reprieve.