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.
Saturday: The Libyan authorities have confirmed the arrest in Mauritania of former Libyan leader Muammar Gaddafi's intelligence chief.
Mauritanian security officials said Abdullah al-Senussi was detained at Nouakchott airport.
Senussi, 63, was Gaddafi's brother-in-law, and has been described as one of his most trusted aides.
He fled Libya when Gaddafi was ousted and killed last year after an uprising and months of fighting.
The International Criminal Court (ICC) issued a warrant for his arrestlast year for crimes against humanity.
France said the arrest was carried out in a joint operation between French and Mauritanian authorities, and President Nicolas Sarkozy said he would request Senussi's extradition.
A French court convicted the former spy chief of involvement in a 1989 attack on a French plane that killed 170 people, and sentenced him to life in prison.
But Libyan authorities are also demanding his extradition.
Mauritania has not signed the ICC's statute, and it is unclear what the country intends to do with Senussi.
Mauritanian security officials said he was arrested during the night as he arrived on a regular flight from the Moroccan city of Casablanca on a false Malian passport.
He has been taken to the offices of the Mauritanian intelligence agency.
Libyan government spokesman Nasir al-Mani told state TV that Senussi was travelling with a young man thought to be his son when he was arrested.
"The Libyan government is making contacts to demand that Abdullah al-Senussi be handed over," said Mr Mani.
Analysts say he could provide the most detailed insights so far into the inner workings of the Gaddafi regime.
Senussi, nicknamed "the butcher", was one of the last significant members of the regime still at large.
He was indicted by the ICC along with Gaddafi and the leader's son Saif al-Islam on 27 June 2011.
Saif al-Islam Gaddafi was captured in November in southern Libya and has been held by former rebels ever since.
The ICC wants him tried in The Hague but the Libyan authorities say he will receive a fair trial at home.
Libyan, Arab and Western sources describe Senussi as a thuggish figure who would beat and abuse prisoners.
He is thought to have been responsible for purges of opponents within the regime in the 1980s and 90s, and for the deaths of 1,200 political prisoners at Tripoli's Abu Salim prison in 1996.
He kept a low public profile during last year's uprising, but reportedly played a key role in attempts to crush the revolt in the eastern city of Benghazi when it began last February.
There have been repeated reports of his death and capture which were later proved false.
Sources in the then opposition claimed he was killed in an attack by rebels in July in the Libyan capital Tripoli but later retracted the claim.
Officials in Niger said in October that he had fled through Niger into Mali, but a month later the new Libyan authorities said he had been arrested in the southern Libyan region of Sabha.
Further reports of his capture came in December but officials were unable to provide pictorial evidence.
· Libya: Public will demand justice in Libya and officials say extradition process already under way; but international concern over fairness of trial
· France: Already sentenced to life in prison in France; President Sarkozy says French authorities involved in arrest; but France may be obliged to hand him to ICC
· ICC in The Hague: Arrest warrant issued in June 2011; but Mauritania not a signatory to Rome statute, so direct transfer unlikely; Libya likely to strongly resist ICC transfer request
Source: BBC News