There is widespread opposition to the proposed D.C. educational tax credit among officials of Washington area private schools -- the very schools that presumably would benefit most from approval of the measure on the Nov. 3 ballot.

Many school headmasters and business managers interviewed this week said that enactment of the $1,200-per-pupil credit would harm the public schools.

At the same time, they said, the proposal would offer no tangible benefits to private schools, many of which already have long waiting lists of students trying to get in. Most private schools could not absorb an added influx of students, they said, though the field would be open to the establishment of fledgling institutions hastily set up to take advantage of the credit.

Moreover, these officials said they doubted that trustees of their nonprofit institutions would risk incurring public wrath by raising their tuition to profit from the tax windfall.

Parents already are spending $4,000 to $4,500 a year to send their children to St. Albans, National Cathedral, Georgetown Day, Sidwell Friends, Holton-Arms and the Sheridan schools, as well as other prominent, independent schools in the area. Tuition is considerably less at Catholic schools, which enrolled 55 percent of the 20,197 Washington children who attended private schools last year.

"My personal view is that it's a very unfortunate proposal," said Gregory Morgan, headmaster of the National Cathedral School, a college preparatory school for girls on Woodley Road NW. "It would be nice if I could take a position in support of a proposal that would help our parents. But it the credit is bad for public schools and bad for private schools."

Thomas J. Camp, business manager for the 530-student St. Albans' School for Boys on Wisconsin Avenue NW, said the proposed tax credit was "a terrible law" that would add to the city's sizeable financial problems.

"What it would do to the public schools is just destroy them," Camp said. "We're in favor of a good public school system and a sound city . . . It the credit would hurt the city's revenues without adding one child to the existing private schools . . . What you'd see is a bunch of fly-by-night schools pop up."

The private school administrators' opposition to the tax credit is the latest twist in the political drama surrounding the initiative.

Earlier this week, Archbishop James A. Hickey of Washington said he would not try to influence Catholic parents on how to vote on the initiative, despite the potential financial boon the credit offers to families with children in parochial schools.

Then on Thursday, the Greater Washington Board of Trade, in an unusual joint press conference with the Greater Washington Council of Churches, the Washington Urban League and the National Conference of Christians and Jews, urged rejection of the proposal, despite a provision enabling businesses to write off 50 percent of their D.C. taxes by contributing to the education of needy students in public or private schools.

The tax credit proposal, known as Initiative No. 7 on the ballot, presumably would offer great assistance to private schools. But administrators interviewed agreed that most private schools would be unwilling or financially incapable of expanding their classrooms, dormitories and athletic facilities to accommodate additional students from the public schools.

Consequently, they said, the primary beneficiary of the tax credit would be middle- and upper-income families that already have children in private schools. A few also mentioned concern about future government meddling in private education if the city began offering financial relief to parents of nonpublic school students.

"The alleged underlying reason for the credit is to offer choice in education," said Solon J. Candage, director of the Sheridan School on 36th Street NW and president of the D.C. chapter of the Council for American Private Education. "But I doubt it will encourage people to start up new schools."

Although sentiment among private school officials apparently runs high against the tax credit, the 250 independent and parochial schools in the area have been reluctant to formally speak out on this politically charged issue.

The Association of Independent Schools of Greater Washington, which includes every major private school in Washington and neighboring Maryland and Virginia, has remained neutral while it polls its 71 members.

However, James W. Lewis, headmaster of the Holton-Arms school for girls in Bethesda, Md., and president of the independent school association, said yesterday he knows of no school that favors the tax credit.

"Elements in the tax credit initiative seem to be of such a nature that they would offset the strength of the public schools," Lewis said. "On that basis, I would not be in favor of it."

Charles Pike of the D.C. Committee for Improved Education, who is managing the campaign for passage of the tax credit, acknowledged yesterday that he had encountered "very strong resistance" from families with children attending the largest, most expensive private schools in the area.

"Whatever the reasons for it, it's not something I would have expected," Pike said. "It's a very interesting anomaly."

However, Pike and other proponents of the tax credit insist they have very strong support among middle- and low-income parents with children in Catholic schools, where tuitions average $582 in elementary schools to about $1,400 in high schools.

Jule Herbert, another organizer for the tax credit, said some inner city private schools "are desperately in favor of this thing."

"Certainly the bigger schools that don't see any impact from this may be happy with the way things are," Herbert said.

The tax credit proposal is the brainchild of the National Taxpayers Union, which has underwritten most of the cost of placing the issue on the ballot and drumming up support for its approval. The amendment has been bitterly opposed by a coalition of D.C. elected officials and labor, church, civic and business leaders.

Under the plan, taxpayers would be able to reduce their D.C. income taxes by up to $1,200 per pupil for expenses they incur at either private or public schools. It would also permit nonparents and corporations to receive tax credits by contributing toward educating low-income youngsters.

Candage, the Sheridan school director, claimed that the proposal was badly worded and ambiguous. Also, he said, the provision allowing businesses to write off taxes by contributing to the education of needy children "clouds the issue" and makes it difficult for the average voter to comprehend.

Craig Channell, an administrator of the Green Acres nursery and grade school in Rockville, Md., challenged proponents of the credit at a public meeting in Northwest Washington Thursday night to explain why private schools "are generally opposed to the credit" if it was so good.

Manuel Dunbar, a federal government clerk-typist and a spokesman for the D.C. Committee for Improved Education, said he assumed that "some of the people in private schools want to maintain the status quo . . . They know they've got a good thing."

After a sharp decline in enrollments between the mid-1960s and early 1970s, enrollment of D.C. students in private schools rose by 22 percent from 1976 to 1980. All of that growth took place in non-Catholic schools, through a modest expansion of existing schools and the opening of new independent schools.

Despite a rapid increase in tuition because of increased costs and higher teacher salaries, demand has been generally strong and the more prestigious schools have had to turn away many applicants.

Among Catholic high schools in Washington, like Gonzaga, St. John's, Archbishop John Carroll, and Immaculate Conception, the tuitions range from $1,000 to $2,350. Elementary school tuitions are considerably less, ranging from $500 to $800.

Among independent private schools, tuition in elementary grades generally ranges from about $2,500 to $3,000, and, in high school, from $3,000 to about $4,300.