For a few tense minutes yesterday it looked as though the D.C. City Council's real estate tax relief bill was going down the drain, victim of a dispute over who should benefit most from its largesse.

Council member David A. Clarke (D-Ward 1) wanted to set the stage for raising the tax rate-on business property, rather than keeping it at the present level, so renters and home owners could get a bigger tax cut than now proposed. His motion lost.

Then Council member Marion Barry (D-At Large) wanted to eliminate an amendment, adopted by the council two weeks ago, that city administrators warned would cause the entire tax billing process to break down - carrying the reform program with it. Barry's motion, which would keep business taxes at their present rate, also lost.

Council members sat there for a few moments, looking around questioningly, whispering among themselves.

It turned out to be Council Chairman Sterling Tucker's chance to get a piece of the action on the tax bill - a measure that, until yesterday, had been fashioned largely by Tucker's two rivals in the current mayoral campaign, Barry and Mayor Walter E. Washington.

Tucker proposed a compromise that, in effect, accepted the thrust of Barry's motion while leaving the door open for future consideration of Clarke's. It passed easily.

Tucker's proposal, formally sponsored by Nadine P. Winter (D-Ward 6), adopted a central feature of the Barry-Washington proposal.

Under it, the uniform tax rate now charged on all property in the city is to be replaced by two separate tax rates, with residential property to be taxed at a lower rate than business property.

Apartment houses would be taxed as business rather than residential property, reversing the amendment adopted two weeks ago by the council at Clarke's urging.

Most crucially, the dual tax rates would be authorized only for this year, and would be reconsidered for next year.

The tax rates for this year have not yet been set. Action is scheduled for July 25, the last council meeting before a month-long recess. That will permit tax bills to be mailed out by Aug. 15.

The rates proposed by both the mayor and Barry are $1.83 for each $100 of assessed valuation for business property, the rate currently charged on all real estate in the city, and $1.54 per $100 on residential property.

Clarke said he had hoped to reclassify apartments as residential property instead of commercial so he could push the rate even higher than $1.83 on other businesses.

Though he gave up his effort yesterday, his own motion and Barry's, seeking to untangle the situation, both failed. That is where Tucker stepped in.

Although yesterday's deliberations resolved some problems with the substance of the bill, they caused a parliamentary delay. Instead of the bill being adopted in final form, as had been expected, it now must come up for a final vote July 25.

Yesterday's debate, notably between Clarke and Barry, often was angry. John A. Wilson (D-Wald 1) said the tax cut was "garbage" in view of the city's unmet needs. Jerry A. Moore Jr. (R-At Large) called it "shadow without substance," and politically motivated.

Approval of the bill was on a voice vote, with no dissents.

On another matter, the council approved an emergency bill by Barry to grant police, firefighters and teachers the same percentage pay increase Oct. 1 that will be received by federal and most D.C. employes under the civil service pay-setting precedure.