They cite a deathbed letter from a man who was a policeman at the time of the 1965 killing, alleging New York police and the FBI conspired in the murder.
Raymond Wood wrote his responsibility was to ensure Malcolm X's security team were arrested days before he was shot dead in Manhattan, his family says.
Three men were convicted of the murder.
The men - all members of the Nation of Islam political and religious movement - were each sentenced to life in prison. One of them has since died, while the other two have been paroled.