A custody battle has erupted between the parents of a woman murdered by her husband, and the husband's sister, over the couple's two young children, officials said Tuesday. The two orphaned children, aged nine and seven, discovered the bodies of their parents, David and Zita Turgeman, in the bedroom of their Jerusalem home on Sunday. The husband left a suicide note in the flat, in which he wrote that he had decided to kill his wife and then take his own life due to a marital crisis, police said. Zita Turgeman's parents, who flew to Israel from Hungary following their daughter's murder, on Tuesday agreed to a police request to carry out an autopsy on their daughter's body, said Dr. Moti Shalem, director of Yad Vashem's International School for Holocaust Studies. The Hungarian-born Zita Turgeman worked at Yad Vashem for the last decade. After the autopsy is carried out, her body will be flown back to Hungary for burial. Shalem stressed that Zita Turgeman's parents, who would like custody of the children, were nevertheless willing to do whatever was "in the best interest" of the children. The children, who are being treated by city social workers, are currently staying at the Jerusalem residence of their late father's sister. The two sides hope to settle the matter outside of court. A Jerusalem municipal spokeswoman said Tuesday that if the two sides fail to reach an agreement, a Jerusalem court will award custody based on the recommendation of city social workers.