The International Criminal Court (ICC) is holding its first public hearing in the case of one of the sons of Libyan leader Col Gaddafi, Saif al-Islam.
He is accused of committing war crimes against the rebels who overthrew his father last year.
His ICC lawyers have argued he will not receive a fair trial in Libya, where he is currently held.
But the Libyan authorities say he should be tried in the country where he is accused of committing crimes.
At the beginning of the two-day hearing, Libyan lawyer Ahmed al-Jehani called for the international community to "be patient", telling ICC judges the Libyan authorities "needed time" to organise a fair trial for Saif Gaddafi.
Mr Jehani told the judges they had not ruled out some level of ICC involvement.
But lawyers for the ICC defence team have accused the Libyan authorities of "empty rhetoric" and of having "aspirations divorced from reality" with regards to holding Saif Gaddafi's trial in Tripoli.
Lawyer Melinda Taylor - who spent nearly a month in detention after she and three other members of the defence team were arrested in Libya after visiting Mr Gaddafi in June - say Libya's lawyers are misleading the ICC, for instance by saying a possible death sentence for Saif Gaddafi could be commuted.
She cited a law passed by Libya's post-revolutionary National Transitional Council which said "no child of Gaddafi will ever benefit from leniency", the AFP news agency reports.
Tug of war
This is the first time the ICC defence team has come face to face with the Libyan lawyers in court, says the BBC's Anna Holligan in The Hague.
The Libyan authorities have made no secret of the fact that they have absolutely no intention of handing Saif Gaddafi over to the ICC, our correspondent says.
If they do want to play by the rules and win the right to try Saif Gaddafi at home, they must convince the judges they can do the job and that Mr Gaddafi will face a fair hearing at home.
Who is Saif al-Islam?
Stylish, English-speaking bachelor
Long seen as likely successor to his father - suggestions he played down
Previously seen as reformist face of his father's regime
Played key role in rapprochement with the West from 2000-2011
Accused of organising brutal crackdown on opposition protests in February
They must show they are conducting their own investigations, and are willing to prosecute Mr Gaddafi for the same alleged crimes that are listed on the ICC's arrest warrant.
One of the lawyers representing Libya, Philippe Sands, has confirmed Mr Gaddafi is still being held by the Zintan Brigade in Libya, adding he will be transferred to a secure detention facility in Tripoli before trial.
The pre-trial session is part of an ongoing battle between Libya and the ICC over where the son of the former Libyan leader should face justice, our correspondent adds.
Mr Gaddafi has been held in the western mountain town of Zintan for almost a year.
During that time, the Libyan authorities have repeatedly rejected requests to hand him over for trial in The Hague.
Source: BBC News