The District government and the Whitman-Walker Clinic dedicated a Logan Circle apartment building yesterday for use by women with the AIDS virus and their families, including some children with the disease.

D.C. Public Health Commissioner Georges C. Benjamin, who was credited for recognizing the need for such a shelter, spoke briefly to a small, wind-swept gathering on 13th Street NW near the circle.

"It is appropriate to emphasize the family when dealing with the crisis of AIDS," he said. "This is a supportive environment for families with AIDS."

The women who moved in with their children have tested positive for the virus or have the disease. Most have little or no income and pay minimal rent. All have children.

"The idea is to keep the family from collapsing," said Scott Sanders, a clinic spokesman. "We want a support system in place before the women become very ill."

One of the eight apartments has been converted into a community room, and another is the home of a resident manager, who also is a social worker.

For some of the women, this is their first contact with other women who carry the virus, Sanders said.

The six apartments are filled, clinic Director Jim Graham said. The building was purchased about a year ago, and the first family moved to the historic mansion in July.

Graham said Whitman-Walker responded to a request from the city for someone to provide housing for families of people with AIDS. He said the clinic, which already runs eight hospices for AIDS patients, discovered it was more economical to buy an apartment building than to rent one.

"We looked all over the city to find space appropriate for families with as many as three and four children, and still stay within a budget," he said.

The building off Logan Circle was a mansion converted to condominiums. However, the units had not sold and the owner was willing to sell the building for $750,000.

Graham said there is a need for more family housing. According to figures released by the clinic, 56 mothers with AIDS are in the Washington area and 56 children under the age of 12 have the virus.

At the ceremony yesterday, the building was dedicated as the Stewart B. McKinney Family Home, named for the representative from Connecticut who died of AIDS complications in 1987. McKinney was a member of the House District committee for 17 years. Funds from the Stewart B. McKinney Foundation are used to keep the house open.

Lucy McKinney, the congressman's widow, spoke at the dedication. "My husband once called President Gerald Ford and asked for a favor, which was granted," she said. "He told the president that now he had something good, he was ready to get something bad. The president said he had something bad to give him and assigned him to the District committee."

Lucy McKinney said her husband was told after one term that he did not have to continue serving on the committee, but he did.

She said critics in his home state often accused him of caring more for the District than he did for Connecticut. "I think he did," she said.