Rent increases of 3.5 to 7 percent starting Jan. 1 to offset the fast-rising cost of oil heating were approved yesterday by the District of Columbia rent control board for tenants of an estimated 57,000 apartments and other rental units.

The unusual stopgap increases, the first of their kind since rent control began in the city in 1974, were authorized by an emergency law passed Oct. 23 by the D.C. City Council at the urging of Mayor Marion Barry.

Under the terms of the law, the city's Rental Accommodations Commission voted yesterday to permit increases up to 7 percent by landlords of projects with 1 to 100 rental units and up to 3.5 percent for landlords of projects larger than 101 units.

No increases will be permitted for units heated by natural gas or other fuels with more stable costs.

The approved increases will not cover the full actual increased cost of heating oil. The rent control office staff estimated that the rising cost of oil increased the total operating cost of an average apartment in the city by 8.3 percent in the 12-month period that ended Sept. 30.

But the actual costs in projects varied widely, rising as much as 17.5 percent in one small project that was surveyed and as little as 5.1 percent in one large project.

In general, officials said, the larger projects -- especially high-rises -- have more efficient heating plants, units with less exposure to the outdoors and better insulation. Smaller units tend to be in the lower rent category, they noted.

Officials said there are 112,000 rent-controlled units in the city, with an estimated 52 percent -- or about 57,000 -- heated by oil.

Under the city housing code, landlords are required to maintain a temperature of at least 68 degrees between 6:30 a.m. and 11 p.m. and 65 degrees at other times.

Under the new increase, a tenant in a 13-unit apartment project on Butternut Street NW near Walter Reed Hospital can expect the current $166-a-month rent to rise to $178, an increase of $12.

A tenant n a 130-unit building on Connecticut Avenue who now pays $226 can expect the rent to rise to $234, an increase of $8. The rent for a $500-a-month unit could go up to $518.

Under the new law, a landlord cannot claim a rent increase that will bring in more money than he is paying for the increased cost of oil. Any overcollection that is discovered later must be repaid to tenants with interest the commission agreed yesterday.

To raise rents, a landlord must give tenants a month's notice. To increase them on Jan. 1, such notices must be given by the end of next week.

The increases are not designed as a windfall for landlords. Under the new law, any money landlords receive will be substracted from the annual across-the-board citywide rent increase that will go into effect next July. The amount of that increase has not been set.

Barry, in proposing the legislation, warned that "many owners of rental housing will be unable to absorb . . . extraordinary price rises and purchase enough fuel" this winter with the rents they are now collecting. John S. Hampton, a rent control staff member, said yesterday that a failure to meet a Jan. 1 date for the increase would mean that "some buildings will run out of oil."

Hampton and other staff members offered the commission several possible formulas for setting the increases. After two hours of discussion Wednesday and more than three hours of sometimes acrimonious debate yesterday, the commission accepted the 3.5 and 7 percent figures proposed by Richard Streeter, a landlord representative on the board. They were adopted by unanimous voice vote.

The commission will meet again Monday to adopt detailed regulations for administration of the increases. In doing so, it also could reconsider the amount of the increases, but is unlikely to do so.