Washington's public schools will have to cut 224 teaching jobs next year unless they receive $7 million more than what city budget planners have tentatively allocated for them, D.C. school Superintendent Vincent E. Reed said yesterday.

The spending figure for 1980 proposed by Mayor Walter E. Washington's budget office is $257 million, Reed told the School Board yesterday. That figure is just $3.8 million above the amount approved for the 1979 fiscal year, which starts Oct. 1.

But Reed said the school system needs $10.8 million for mandatory increases, including longevity pay for teachers and legally required improvements in special education for handicapped children.

Unless all the money the schools need is granted, Reed said, there will have to be "major cutbacks in educational programs," including the loss of the 224 teaching jobs.

Comer Coppie, the D.C. budget director whose office established the tentative allocation last month, said the figure was part of an effort to hold down spending throughout the city government to avoid higher taxes.

Coppie said the school system expects its enrollment to go down next year by about 5 percent, which will probably allow any teacher cutbacks to be absorbed without larger classes.

"Within our ability to meet all the city's needs in 1980, we have given the school system a fair mark" Coppie said. "Beyond that, it's up to them to allocate the money."

Betty Ann Kane, chairman of the school board's finance committee and a candidate for City Council, said cuts in school spending requests over the past two years already have forced the school system to curtail advanced courses and other specialized programs having small enrollments.