A copy of the letter, seen by Reuters, said that Muammar Gaddafi and his son Mo'tassim were "murdered in the most horrific fashion with their bodies thereafter displayed and grotesquely abused in complete defiance of Islamic law".

"The images of this savagery were broadcast throughout the world, causing my client severe emotional distress," said the letter from Nick Kaufman, who represents Aisha Gaddafi.

"To date, neither Ms. Gaddafi nor any member of her family has been informed, by your office, of the initiation of an investigation into the circumstances surrounding the brutal murders," the letter said.

Muammar Gaddafi and Mo'tassim were captured in their home town of Sirte in October, two months after rebels seized the capital Tripoli and put the longtime Libyan leader and his relatives to flight.

They were killed soon after their capture while in the custody of fighters loyal to the country's new leadership, in circumstances that have not been fully explained.

Gaddafi's daughter Aisha fled with other family members to neighbouring Algeria in August.

The ICC, based in the Hague, earlier this year issued arrest warrants for Muammar Gaddafi, another son, Saif al-Islam, and the former Libyan intelligence chief Abdullah al-Senussi, for crimes against humanity.

In the letter, Aisha Gaddafi's lawyer asked if the ICC prosecutor's office was investigating the killings of her father and brother, and if it was taking steps to make sure the Libyan authorities themselves were investigating the matter.

The letter also asked whether the ICC was looking into what reports said at the time was a NATO air strike on Gaddafi's convoy moments before he was captured.

"Is your office investigating the attack allegedly carried out by NATO forces in order to determine whether individual criminal responsibility should be assigned for an unlawful military attack?" the letter asked.