Landlords in the District of Columbia will be permitting to raise rents to cover the fast-rising cost of fuel oil they must buy to supply heat to tenants.

The D.C. City Council voted 11 to 2 late Tuesday night to grant the increase proposed by Mayor Marion Barry. The measure, adopted as emergency legislation, will go into effect as soon as it is signed by Barry. Rent increases porbably will come on or after Jan. 1.

In seeking the measure, the mayor warned that "many owners of rental housing wil be unable to absorb . . . extraordinary price rises and purchase enough fuel" this winter with the rents they now collect.

The proposal was bitterly opposed by a group of organized tenants, who lobbied vigorously against its passage. Spokeswoman Evelyn Onwuachi contended at a news conference that it would increase already exorbitant profits for "those with wealth and property." She said it would be challenged in court.

Under the measure, landlords will be able to raise rents based upon a formula reflecting the percentage rise in oil heating costs as a part of the total operating costs of rental properties. Other forms of heating are not covered.

D.C. Rental accommodations Office estimated that a typical low-rent apartment dweller paying $238 a month would face an increase of $12.66.

However, money received under the increase would be subtracted from the across-the-board annual rent increase scheduled for next spring under the rent control law. The amount of that increase has not yet been decided.

Raymond J. Hower, president of the Washington Board of Realtors, said he was disappointed by the council vote because the measure did not go far enough. Housing industry leaders supported amendments offered by Betty Ann Kane (D-At Large) and Willie J. Hardy (D-Ward 7) that would have permitted landlords to recover the full dollar cost of increased oil prices. The amendments were rejected by a council majority.

Council members Hilda Mason (Statehood-At Large) and Whlhelmina J. Rolark (D-Ward 8) opposed passge of the bill.