John Graham is appealing his 2010 conviction in the slaying of Annie Mae Aquash.
His attorney told the South Dakota Supreme Court on Monday that he didn't have sufficient time before trial to question the court's decision to allow the case to be moved.
John Murphy also contends several witness statements shouldn't have been allowed.
Prosecutors say Graham and two other AIM activists killed Aquash because they thought she was a government informant.
Attorney General Marty Jackley says there wasn't anything wrong with moving Graham's case or with the witness testimony.
Graham is from the Southern Tutchone First Nation in Yukon.
Aquash was a member of the Mi'kmaq tribe of Nova Scotia.
She was active in AIM, a group started in the late 1960s to protest the U.S. government's treatment of American Indians and demand the government honour its treaties with Indian tribes.
The movement grabbed national headlines with its 1972 takeover of the Bureau of Indian Affairs headquarters in Washington and, during the following year, its 71-day occupation of the reservation town of Wounded Knee, South Dakota.
Graham was sentenced to life in prison in January 2011.
During five days of testimony in late 2010, witnesses had said they saw Graham and two other AIM activists take Aquash from a house in Denver and eventually to the Pine Ridge Indian Reservation.
Arlo Looking Cloud, who was convicted in Aquash's slaying in 2004, testified that he watched Graham shoot Aquash with a .32-calibre pistol.
What still isn't known are the exact circumstances behind Aquash's killing. Authorities believe AIM leaders ordered her death because they thought she was helping the government, which officials have denied.
No AIM leader has been charged in her slaying, and several people involved with AIM have denied their own involvement.