In a move sure to create an early problem for the incoming Barry administration, the District of Columbia's housing department has formally proposed to end the two-year old moratorium on converting low-rent apartments into condominiums.

The proposal comes at a time when tenant groups are insisting that the city's rental market is tightening rather than loosening, making it hard for older people and large families to find places to live.

The moratorium's end would be triggered by the official certification of figures showing that 4.73 percent of the privately owned low-rent units in the city were vacant at the time of a controversial 1976 survey.

When the council voted the moratorium that year it decided to allow condominium conversions again if it were found that at least 3 percent of the low-income units were vacant. There is no moratorium on converting high-rent units.

Procedurally, the earliest the certification could take effect is Jan. 19, by which time Marion Barry will have replaced Walter E. Washington as mayor. Barry has said he intends to fire Washington's appointee as the director of the Department of Housing and Community Development, Lorenzo W. Jacobs Jr., who announced the planned adoption of the 4.73 percent figure.

Council member Hilda Mason (Statehood-At Large), deploring Jacobs' proposal, said she plans to introduce emergency legislation next month to raise the triggering vacancy rate to 5 percent.

Mason sponsored legislation drafted by tenant groups this year that included 5 percent trigger, but it died at the end of the council session without being considered.

There are between 170,000 and 180,000 rental apartments and houses in the city, but no statistics were available yesterday on how many would fit in the low-rent category.

In Washington, the official definition of low rent covers some apartments costing tenants as much as $408 a month. That is the maximum for a three-bedroom unit. The maximum for an efficiency unit is $221, for a one-bedroom unit $267 and for a two-bedroom unit $314.

In preparing for the certification, the housing department originally proposed to adopt a vacancy rate of 4.88 percent, based on a survey conducted in 1976 by the Metropolitan Washington Council of Governments.

At a hearing last April, numerous witnesses representing tenant groups attacked the accuracy of the figure. They contended the survey was conducted entirely by mail, did not consider such factors as overcoming, habitability or apartment turnover rates, and was generally unreliable.

The only support for the survey findings came from the spokesman for an apartment owners' group.

Jacobs, in circulating an announcement of his plan to certify the slightly lower 4.73 percent figure, did not explain why it has been changed or why eight months had elapsed between the hearing and his proposal. One departmental officer, to whom a reported was referred, said he did not know the answers.