Libya has formally requested the handover of Col Gaddafi's former intelligence chief Abdullah al-Senussi, following his arrest in Mauritania.
A spokesman for the new government in Tripoli "insisted" Senussi be extradited to Libya to face trial.
However, he is also sought by the International Criminal Court (ICC) on charges of crimes against humanity.
France also wants to extradite him in connection with a bomb attack on a plane in 1989.
Mauritania has already said it wants to carry out its own investigation before considering any extradition requests.
Senussi was held at the airport in the Mauritanian capital, Nouakchott, after flying in from Morocco using a false passport, officials said.
However, Mauritania has not yet provided any evidence of his arrest.
It is believed he is being held at the offices of the Mauritanian intelligence agency.
Senussi, 63, fled Libya last year as Colonel Gaddafi's regime began to crumble.
'Gaddafi's black box'
"We insist that Senussi is extradited to Libya," said Mohammed al-Harizy, spokesman for Libya's National Transitional Council.
"There are demands from the ICC and France to get Senussi, but the priority is to deliver Senussi to Libya."
The arrest provoked strong feelings on the streets of Tripoli on Saturday.
"Senussi is Gaddafi's black box, he has a lot of information," Tripoli resident Mustafa Jhyma was quoted by Reuters as saying.
"He has blood on his hands, he should be brought here and tried in Libya."
Human Rights Watch and Amnesty International both said that Mauritania was bound by the UN Security Council to co-operate with the ICC, even though it has not signed up to its statute.
Hassiba Hadj Sahraoui, Amnesty's deputy director for North Africa, said in a statement that the Libyan justice system remained "weak and unable to conduct effective investigations into alleged crimes".
UK Foreign Secretary William Hague also urged all involved to co-operate with the ICC.
The ICC issued an arrest warrant for Senussi last June, saying he was an "indirect perpetrator of crimes against humanity, of murder and persecution based on political grounds" committed in the eastern city of Benghazi.
He could also be held to account for the massacre of more than 1,000 detainees at a Libyan prison in 1996.
A French court has already convicted the former spy chief in absentia of involvement in a 1989 attack on a French plane that killed 170 people, and sentenced him to life in prison.
Senussi, nicknamed "the butcher", was one of the last significant members of the Gaddafi regime still at large.