Libya's interim PM unveils new government line-up
Libya's interim PM has named a new transitional cabinet, the first step to forming an elected government.
The new government is tasked with drafting a constitution and holding democratic elections by next June.
Correspondents say the line-up is aimed at soothing the rivalries between regional factions.
Meanwhile, the International Criminal Court has accepted that Col Gaddafi's captured son Saif al-Islam will be tried in Libya, not The Hague.
ICC chief prosecutor Luis Moreno-Ocampo said the court had issued an arrest warrant for Saif al-Islam on war crimes charges because Libya's justice system was not up to it.
He said this was no longer the case, but that the ICC would help in any trial.
Libya's interim Prime Minister, Abdurrahim al-Keib, was elected by the National Transitional Council (NTC) last month.
The NTC is a coalition of rival factions that came together to oust Col Gaddafi, who was killed in his birthplace, Sirte, on 20 October.
Mr Keib gave the post of defence minister to Osama al-Juwali, the local military commander of the western town of Zintan.
On Saturday, his fighters captured Muammar Gaddafi's son Saif al-Islam.
The interior ministry went to Fawzi Abdelal, one of the Misrata rebel leaders, whose fighters captured Muammar Gaddafi in October.
Other key appointments include Abdurrahim Bin Yazza - a former executive with the Italian oil giant ENI - as head of the oil and gas ministry and Ashour Bin Khayal, as interim foreign minister.
There had been suggestions that Libya's deputy UN ambassador, Ibrahim Dabbashi, was a contender for the foreign minister post, but he was not in the final line-up.
The BBC's Rana Jawad, in Tripoli, says the first test of the new government will be to successfully centralise Libya's political and military powers.
Only then will the government be able to proceed with drafting a constitution and eventually hold Libya's first democratic elections in its modern history, our correspondent says.
Saif al-Islam had been on the run since NTC forces took Tripoli in August, six months into the uprising.
Since he was arrested on Saturday, Libya's new government has insisted that he will face a fair trial locally.
As Mr Moreno-Ocampo arrived in Libya, Libya's Justice Minister Mohammed al-Allagui said: "In a nutshell, we are not going to hand him over," reported the AFP news agency.
The ICC has also issued an arrest warrant for Col Gaddafi's spy chief Abdullah al-Sanussi, who was regarded as the late leader's right-hand man - and one of the regime's most-feared figures.
Libya's government says Mr Sanussi, a brother-in-law of Col Gaddafi, was arrested at his sister's home in the southern town of Sabha on Sunday.
Mr Keib has promised that Saif al-Islam will receive a fair trial after concerns were raised about the possibility of ill-treatment given the killing of Col Gaddafi after his capture in Sirte.
The International Red Cross said on Tuesday that it had visited Saif al-Islam, who's being held in Zintan.
A Red Cross spokesman, Steven Anderson, said he appeared to be in good health, but would give no more details.
Col Gaddafi was overthrown and his supporters defeated after a nine-month insurgency that began in the eastern town of Benghazi and eventually swept across the rest of the country.
Militias in different areas, joined by defectors from the army, were aided by Nato forces who bombed Col Gaddafi's forces under a UN mandate to protect civilians.