The D.C. City Council's Finance and Revenue Committee approved legislation yesterday to set up a three-level real estate tax system that would reduce an expected tax increase on rented homes and eliminate a windfall tax reduction on commercial properties.

The proposal would expand the present two-level real estate tax system that divides properties generally into residential and commercial categories.

Council member John A. Wilson (D-Ward 2), the committee chairman, also disclosed two proposed steps to increase tax revenues and make up a projected $104 million shorfall in the city's budget for the 1981 fiscal year, which starts Oct. 1, 1980.

Wilson said he may recommend eliminating the $9,000 exemption that reduces the annual tax bill on each owner-occupied home in the city by $140. The owners would continue to benefit from a lower tax rate, Wilson asserted.

He also introduced a bill to charge a 5 percent sales tax on a number of now-exempt items, including theater tickets, laundry and dry cleaning services and barber and beautician services, among other activities.

The tax would charge, under the bill, on services by employment and collection agencies, private detectives and interior decorators.

Wilson estimated that the extended sales taxes would raise up to $15 million a year. He announced a hearing on the bill for 10 a.m. June 5 at the District Building. The real estate tax measure approved by the committee would change the two-level tax system that went into effect last year. Under that system, the city began taxing residential properties at a lower rate than apartment buildings and commercial properties.

However, rented homes and most apartment buildings containing up to five units were classified as residential. Mayor Marion Barry recently recommended that these units be taxed at the higher commercial rate. The D.C. audiotr's office reported that the shift would raise the tax on each affected rental unit by an estimated $183 annually while reducing taxes on many valuable commercial properties.

For example, the auditor estimated that the tax on the Watergate-the city's second most valuable private property-would drop by $134,165.

Yesterday's committee action, a recommendation to the full council, rejected Barry's proposal and calls for putting owner-occupied residential units in one class of property, rented residential properties in a new second class and commercial properties in a third, starting next fall.

Barry had said in his original proposal that he expected to recommend a residential tax rate of $1.36 and a commercial tax rate of $1.65 for each $100 of assessed value. Wilson said these rates probably would be changed.