D.C. Mayor Marion Barry gave his approval yesterday to a comprehensive plan designed to improve the District's approach to providing services to the city's growing number of homeless families.

"Our commitment to decreasing homelessness is unwavering," Barry said during a news conference. "We are especially committed to altering the condition of homeless families. This problem must not be permitted to become a multigenerational dilemma with associated social and economic losses."

Currently, the District government's homeless shelter programs provide hotel rooms or apartments for 287 homeless families, including more than 500 children. During 1986, the number of families who sought housing under the city's emergency shelter program increased by more than 500 percent.

The comprehensive plan for homeless families, which was developed by the Department of Human Services and the mayor's Commission on Homelessness and announced in January, calls for decreasing the city's use of hotels and motels on an emergency basis. Under the plan, the city would acquire 200 temporary apartment units where families would receive comprehensive social services, including counseling in budget management, housekeeping, child care and nutritition.

To implement the plan, Barry said the city will hire 67 social workers to work with families, provide 500 training positions in the Department of Employment Services for the heads of homeless families and turn some homeless families into homeowners by renovating 20 houses.

In addition, Barry said coordination among government departments will be increased to improve services to the homeless. For example, Barry said, $2.2 million that had been set aside for people with emergency housing needs will be used instead to provide 600 units of low-income housing for homeless families.

Department of Human Services officials were unable to say how much the plan will cost, or whether it will require an additional D.C. Council appropriation.

The city's approach to housing homeless families has been criticized as costly by council member H.R. Crawford (D-Ward 7) and others. Crawford has introduced a bill that would limit the stay of homeless families to 180 days in emergency government shelter facilities.