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 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 after flying in from Morocco using a false passport.
Senussi, 63, fled Libya last year as Colonel Gaddafi's regime began to crumble.
Senussi, nicknamed "the butcher", was one of the last significant members of the Gaddafi regime still at large.