But Libya said that letting Seif al-Islam Gaddafi go on trial outside the country would worsen unrest gripping the country and would even be a threat to his life.
Bensouda called on the UN Security Council to press Libya over the deceased strongman's son, and also for international help including "telephone intercepts" and information on money transfers linked to the Kadhafi family and their associates.
The ICC and Libyan government have been wrangling over Seif al-Islam since the overthrow and killing of his father in October 2011.
Seif al-Islam is held by a brigade of former rebel fighters and many rights groups say he will not get a fair trial in Libya where the authorities face mounting security concerns amid attacks on government and judicial targets.
Also Read
Libya has said it will give the ICC new information on the Seif al-Islam case. But Bensouda said it was "fundamentally important" for the Security Council to pressure Libya over the case and for all states to respect ICC warrants.
"Political considerations have no place in law, impartially and independently applied. I strongly urge the government of Libya to surrender Seif al-Islam Gaddafi to the court without further delay," the chief prosecutor added.
"That would then destabilize social peace which is quite precarious, and indeed it might constitute a threat to the lives of" Seif al-Islam and Gaddafi's intelligence chief Abdullah al-Senussi, Dabbashi told the Security Council.
The ICC has agreed to let al-Senussi be tried in Libya. And Bensouda announced that she would not appeal that decision.
"The challenge is now for Libya to demonstrate to the world that al-Senussi will receive a genuine, fair, impartial and speedy trial that respects all his rights," Bensouda said.
The ICC is still investigating several cases in Libya linked to Gaddafi's efforts to crush the uprising against him.
Bensouda said that Security Council and international help would be "crucial for the collossal task of collecting evidence to untangle the modus operandi of the networks responsible for committing crimes.