Mayor Walter E. Washington, expressing sharp criticism of the D.C. City Council, announced yesterday that he would allow a three-year extension of the District's controversial rent control system to go into effect - without his signature.

The mayor, whose veto of a previous rent control measure drew both criticism and praise, appeared to have sought out a cautious, middle-ground position on the politically divisive issue yesterday. He said he had cdecided not to veto the Council-approved legislation because he favors a continuation of rent control, but he attacked the Council's measure, terming various parts of thebill legally unsoung, "misleading" and possibly "illusory."

The complex rent control measure - enacted after months of legislative demonstrations - would authorize annnual rent increases for most of the city's 180.000 rented apartments and houses. More than 400,000 D.C. residents, over half the city's population, are estimated to live in rented housing.

Under the legislation, most tenants in the city would probably face rent increases next year varying from 2 to 10 per cent. Landlords would, however, be permitted to raise rents more sharply if they can prove they are confronted with financial hardship. A recent survey by city officials showed that rent increases averaging 39 per cent have been authorized under hardship proceedins.

In 1979 and 1980, across-the-board rent increases permitted under the new legislation would be partly linked to rises in the Labour Department's Consumer Price Index. The specific amounts of such increases would be set by the D.C. Rental Accommodations Commission, a board that oversees the rent control program.

The earliest rent rises allowed under the new legislation appear likely to be put into effect by many landlords next April, May or June. The rent control extension will become law only after Congress, which recessed last night until Jan. 19, has been given a period of 30 "legislative" days - normally about two months - to veto it. Congress has never disapproved a bill passed by the city's home-rule government. Tenants, in addition, must be allowed 30 days' notice before their rents may be raised.

The legislation that the mayor allowed yesterday to take effect without his signature would extend rent control until Sep. 30, 1980, apparently assuring a continuation of the controversy and court battles that have engulfed the program since it was begun here three years ago. Lawyers and government officials have both said they expect the new measure to face renewed legal challenges by city landlords over a number of issues, including those citied by the mayor in his message yesterday.

Tenant groups have supported rent control, calling it a stopgap measure that protects low and moderate-income renters from rent increases they cannot afford. Tenant advocates have expressed mixed views about the newly enacted rent control extension, praising it for continuing the rent control system but criticizing it for permitting rent increases that they regard as too steep.

Real estate and other business organizations have attacked rent control, arguing that it deprives property owners of their right to earn a reasonable income, deters construction of new rental housing and leads to deterioration of existing apartment houses. Spokesmen for the city's landlords have criticized the new rent control extension, largely because it has delayed until next year rent increases that had been designed to offset rises in costs incurred by landlords during 1976.

Rental control has also sparked a continuing battle between Mayor Washington and the City Council, which includes some of his political critics and two of his prospective rivals for mayor in next year's Democratic primary - City Council Chairman Sterling Tucker and at-large Councilman Marion Barry. Neither Tucker nor Barry has formally announced his candidacy, and the mayor has not yet announced whether he will seek re-election.

In October, the mayor scored what some of his supporters viewed as a political coup when he vetoed a Council approved emergency bill that would have authorized immediate rent increases for most of the city's tenants. The veto angered many concerned with real estate and other businessmen. Recently, however, the mayor has appeared to have adopted a political strategy aimed at winning support from poor, black and elderly D.C. residents, while at times overlooking the city's predominatly white business community.

In allowing the Council-approved extension of rent control to go into effect without his signature yseterday, the mayor took advantage of a prvision of the city charter that permits bills to become law unless they are vetoed by the mayor within 10 working days. The city's existing rent control law will expire Jan. 29. The Council is expected to extend it temporarily by emergency legislation. This would keep rent control in effect until the three-year rent control extension has cleared Congress.

Mayor Washinton's criticism of the Council's latest rent control measure was quickly rejected by Council Chairman Tucker, who issued b point-by-point rebuttal last night.

The mayor focused his criticism partly on a rent subsidy plan that was incorporated in the rent control measure in an attempt to cushion the impact of the proposed rent increases for low-income, elderly and disabled renters. The multimillion dollar program is designed to offer subsidies amounting to as much as 15 per cent of the rents paid by low-income tenants.

The mayor asserted that, while he favors rent subsidies for the needy, the Council's plan was "misleading" because it would not provide aid for many poor persons - specifically tenants who also receive welfare payments.

He added that the city's fiscal advisers had found the proposed subsidy program to be possibly "illusory" because it is uncertain how it will be financed. No city funds have yet been set aside to pay for the subsidies. The mayor said, however, that he will seek to remedy this apparent shortcoming by proposing a budget amendment soon.

Tucker rejected the mayor's complaints, charging that the mayor had failed to "recognize the intent" of the subsidy plan. In addition, Tucker announced that he himself would introduce $6.6 million to finance the subsidy program for its first year.

The mayor also charged that the Council "chose to ignore" a series of legal defects in its legislation. These he noted , had been cited by the mayor's legal advisers before the Council passed the measure last month.