(CNN) -- U.N. war-crimes prosecutors are leaving an investigation into the death of ousted Libyan strongman Moammar Gadhafi to Libyan authorities for now, they said Tuesday.
Gadhafi's daughter Aisha pressed the International Criminal Court's prosecution office last week to look into the October death of her father and brother Mutassim. In a written response to her attorney, the prosecution office said it would decide whether it needed to mount its own probe next year.
"The Office of the Prosecutor will review such activities and make its findings public in May 2012 during the prosecutor's second report to the United Nations Security Council," the response read. "During this report, the OTP will present its strategy with regards to future investigations of alleged war crimes committed in Libya, including the killing of Moammar Gadhafi."
Any International Criminal Court investigation "will depend on the activities of the Libyan national authorities and whether they are genuinely carrying out such investigations," the letter states.
But Aisha Gadhafi's attorney, Nick Kaufman, said his client believes the ICC needs to be involved now to make sure a "professional investigation" takes place.
"Aisha Gaddafi questions to what extent an objective and effective investigation which meets international standards -- including ballistic and forensic analysis of the crime scene and preservation of other exhibits -- can take place if the prosecutor delays his involvement until the next report to the UNSC," he said in a statement to CNN.
Gadhafi ruled Libya with an iron fist for nearly 42 years before being overthrown in August. Libya's transitional government said he was killed in the crossfire between its fighters and Gadhafi loyalists after he was captured in his hometown of Sirte on October 20.
In a December 13 letter to prosecutors, Kaufman said Moammar and Mutassim Gadhafi "were captured alive at a time when they posed no threat to anyone," only to be "murdered in the most horrific fashion" after their capture.
An autopsy determined the 69-year-old fugitive died from a gunshot wound to the head, but the pathologist who performed the procedure would not reveal whether the wound was inflicted at close range or from a distance. The bodies of the ousted ruler, his son and his longtime defense minister were put on display in a meat-market refrigerator for several days before being buried.
Aisha Gadhafi fled to Algeria along with several other family members as the regime crumbled in August. She is a lawyer who assisted in the defense of ex-Iraqi dictator Saddam Hussein, who was hanged in 2006, and a onetime U.N. goodwill ambassador.
Gadhafi's son and top aide, Saif al-Islam Gadhafi, was captured in November, Libyan authorities said. Senior Libyan military officials said they believed he was trying to make his way to neighboring Niger, where a brother, Saadi, was granted asylum.
Gadhafi's youngest son, Saif al-Arab, was reported killed in a NATO airstrike in April. And son Khamis Gadhafi, who led an army brigade blamed for the massacre of prisoners in a warehouse outside Tripoli, was killed in a late-August battle in northwestern Libya, rebel commanders said.