Despite a high demand and an obvious need to house large numbers of low-income families, the District of Columbia has stumbled seriously in administering its federally funded rent subsidy program, D.C. Auditor Matthew S. Watson reported yesterday.

In a separate report, Watson called upon the city government to reconsider plans to raise fees it pays to about 800 people who provide foster homes for Washington children. He said a proposed $1.4 million annual increase in payments is not warranted.

In his report on the rent subsidy program, Watson said that "as a result of the lack of control" by the D.C. Department of Housing and Community Development, "the program has fallen short of the potential."

The report said the U.S. Department of Housing and Urban Development has authorized the city to use federal funds to pay one-quarter of the rent of 570 units but has leased only 45 percent of them.

But contrast, the report said, Montgomery County has leased 63 percent of units to which it is entitled.

The city's failure to take steps to lease more units, including obtaining permission to pay higher rents in some cases, "reveal a lack of leadership and concern" by the city department, the report said.

The report, requested by Nadine P. Winter (D-Ward 6), who chairs the City Council's housing committee, was issued at a time when housing is a major issue in council and mayoral campaigns, including Winter's own effort to gain reelection.

Deputy Auditor Carl H. Bergman said the city department failed to respond to a draft of the report by an Aug. 25 deadline, so the report was issued without departmental comment. Lorenzo W. Jacobs Jr., director of the department, could not be reached for comment.

In his report on foster homes, Watson said an average 36 percent increase in board payments - setting the monthly rates between $253 and $265 per child - is not called for. He said the proposed increase is double the increase in the cost of living since the last increase was granted in 1974.

The auditor did say, that special higher rates may be warranted for children who have physical, mental or emotional handicaps.

Albert P. Russo, director of the Department of Human Resources, which administers the program, contested the auditor's recommendation. He said the department has a formal procedure to set special rates for handicapped children.