PINE RIDGE INDIAN RESERVATION, S.D. — Forty years after the siege at Wounded Knee by members of the American Indian Movement, the Oglala Sioux tribe has demanded that the federal government reopen dozens of cases it says the F.B.I. may have mishandled decades ago.

Tribal leaders say that as many as 75 people were killed on Pine Ridge during a three-year period of internecine violence that followed the 71-day Wounded Knee standoff with federal troops in 1973, a time that came to be known on the reservation as the “reign of terror.”

The federal government has declined so far to re-examine the cases....