Private school students would get triple the federal aid of many urban public school students by 1984 if the Reagan administration's tuition tax credit bill passes, opponents of the measure charge.

A coalition of public school lobbyists said the administration proposal would raise private school aid from $43 per student in the 1980-81 school year to $329 per student in 1984-85.

At the same time, administration proposals to reduce other federal aid to education would cut in half the per pupil expenditure in 65 urban districts in 29 states, from $206 in 1980-81 to $105 in 1984-1985, they contend.

The study counted only direct aid to schools, such as money for extra teachers for disadvantaged children or special services for the handicapped. It did not include food aid, such as subsidized lunches.

Locally, in Fairfax County, the study shows that direct public school aid would drop from $115 to $100 per student over the same period, while private aid would jump from $13 to $302 per student.

Opponents released the study Wednesday as the Senate Finance Committee tried to approve the bill. Tuition tax credit backers, such as Sen. Bob Packwood (R-Ore.), say the proposal would merely equalize federal support for public and private education.

Robert Smith, executive director of the Council for American Private Education, challenged the figures. He said he wondered where the study got its figures on the current amount of federal aid to private schools since he knows no one who collects the data. He said also amendments to cut the cost of the proposal would make the study's final figures "way off."

Final consideration of the bill was postponed because the committee was busy with the administration's $98.3 billion tax bill and some Democratic members expressed concern about its anti-discrimination clauses.

Sen. Robert J. Dole (R-Kan.), the committee chairman, has indicated that he will propose amending the bill to cut its cost by reducing the maximum credit from $500 to $300 per child and by lowering the ceiling on family income eligible for the full credit. An aide to Sen. Bill Bradley (D-N.J.) said yesterday he will offer an amendment to ensure the Internal Revenue Service, as well as the Justice Department, has power to enforce the anti-discrimination provisions.

The authors of the aid study, the Council of the Great City Schools and the American Association of School Administrators, acknowledged that adding federal food aid to the public and private school totals might make them more equal. But they said the estimated difference in direct aid shows that the administration proposal "is one more avenue for taking from the poor and giving to the rich, a federal approach that is as ill conceived as it is deplorable."

Backers of the concept said the study figures are misleading because the aid to private students would be to parents, not schools. They noted that many private school students attend parochial or other schools in the inner cities, not exclusive prep academies.