The D.C. City Council yesterday moved one step closer to extending rent control on about 112,000 Washington apartments for the next five years, after voting to let stand a controversial amendment that allows a 10 percent rent increase whenever apartments are vacated and rerented.

The vote clears the way for final approval of the complex legislation at the council's next meeting Dec. 9. If the bill is passed then, as expected, it must be signed by the mayor and reviewed by Congress before becoming law April 30, when the current rent control law expires.

In other action yesterday, the council backed off its previous decision to $26.8 million to Mayor Marion Barry's proposed 1982 budget for pay raises for city workers. The mayor had vetoed that part of the council-backed budget because $20 million of the pay raise money came from a fund Barry had set aside for the sole purpose of repaying the city's long-term debts.

Following a prearranged compromise reached last week between Barry and council member John Wilson (D-Ward 2), the council yesterday voted to slice the pay raise money to $16.8 million for pay increases and restore the $10 million difference to the mayor's debt repayment fund.

On the rent-control legislation, the council's vote brought to a near end the year-long political controversy over what to do when the current rent controls expire. Council members were lobbied, on the one hand, by landlords, developers and housing experts who told them repeatedly that rent control was responsible for eroding the city's housing supply, scaring away potential developers and making it unprofitable for landlords to maintain their apartments.

Highly organized city tenant groups, on the other hand, complained that landlords, free of controls, would raise their rents so fast and so high that poor and middle-income renters would be priced out of their homes.

The bill passed yesterday was supposed to be a balance between the two opposing positions, keeping controls in place to please the tenants while trying to provide some financial encouragement to landlords and developers.

The bill allows landlords a 10 percent profit each year, compared to the 8 percent currently allowed, and it ties future automatic annual rent increases to the Washington area's consumer price index, with increases not to exceed 10 percent.

Tenants, however, saw the new bill as tilted too much toward the landlords, especially after council member John Ray (D-At-Large) introduced his amendment at the bill's first reading 12 days ago, allowing landlords to increase by 10 percent the rent they can charge on vacated apartment units.

Voting with Ray on his amendment yesterday were council members Jerry A. Moore (R-At-Large), Betty Ann Kane (D-At-Large), Charlene Drew Jarvis (D-Ward 4), Nadine Winder (D-Ward-6), Willie Hardy (D-Ward-7) and Chairman Arrington Dixon. Voting against were members David Clarke (D-Ward 1), Polly Shackleton (D-Ward 3), William Spaulding (D-Ward 5), Wilhelmina Rolark (D-Ward 8), Hilda Mason (Statehood-At-Large) and Wilson.