The Army announced it is closing and demolishing a child-care center at its base at the Presidio after allegations that as many as 60 youngsters were sexually abused there.

Maj. Greg Rixon, an Army spokesman at the Pentagon, said the Presidio Child Development Center would be closed Friday and a new center would be opened by April.

A Presidio spokesman, Bob Mahoney, said the closing, which was disclosed Saturday, was for ''health, safety and sanitation reasons, and not as a result of allegations of child abuse.''

But Representative Barbara Boxer, Democrat of California, said Army officials had told her earlier that some children were afraid to return to the center. Dwindling Attendance