Alawi's clients Abdul Jalil al-Mudad, Muhammed al-Muqdad and Abdul Wahhab Husain received life sentences, he said.
Among other things, Abdul-Jalil said shariah would be the "basic source" of all legislation.
In an attempt to quell the protesters' anger, Jalil fired six secular members of the NTC.
His murder was widely blamed on an Islamist militia and prompted Mr Abdel Jalil to sack several ministers.
Mr Abdel Jalil commands respect both from Islamists, towards whom he is sometimes said to tilt, and the secularists.
Mr Jalil did not elaborate on the identity or motivations of the assailants.
The special representative of the secretary general of the United Nations to Libya, Ian Martin, smiled as Jalil announced the handover.
Jalil Lespert plays Franck, an ambitious young student who comes home from Paris to spend time at the local steel-pressing plant.
England made a shaky start in reply when Taylor was caught by Javeria Khan off Qanita Jalil in the fifth over.
Interim Prime Minister Abdul Rahim al-Kib appeared moved as he hugged Jalil.
They are led by Mustafa Abdul Jalil, a calm and consensual technocrat.
At least 146 people were also wounded in the explosion and 32 of them remain in serious condition, said Pakistani surgeon, Jalil Qadir.
Mr Jalil expressed Libya's gratitude for the help received from Nato forces and other foreign forces, as well as the Libyan rebel forces.
His deputy, Ali Tarhouni (pictured with Mr Abdel Jalil behind him), who holds the oil and finance portfolios, is set to replace Mr Jibril.
On Saturday protesters laid siege to the National Transitional Council offices in the city while Mustafa Abdul-Jalil, the head of the NTC, hid inside.
Abdul Jalil said he was open to compromise, but that it was too close to Election Day to increase the east's representation in the congress.
It is up to the new ruling authorities, led by the avuncular chairman of the transitional national council, Mustafa Abdul Jalil, to balance the two.
He then spoke with Mustafa Abdel Jalil, Chairman of the National Transitional Council (NTC) of Libya, and Mahmoud Jibril, Head of the NTC Executive Committee.
The chairman of the NTC, Mustafa Abdul Jalil, told reporters last week that delegations had been dispatched to the east to negotiate with those making the demands.
And I want to thank President Jalil for his remarks and for all that he and Prime Minister Jibril have done to help Libya reach this moment.
And she said in the fall, she met with Mustafa Abdul Jalil, chairman of Libya's Transitional National Council, who has said he has proof Gadhafi ordered the bombing.
Members of the 200-person body took the oath of office en masse, and Jalil told them what they already knew: they face major challenges in security and disarmament.
Varying accounts of how he was killed were then given by officials including Mr Jalil, who chaired the now-dissolved National Transitional Council (NTC) when Gen Younes was shot.
BBC: Abdel Fattah Younes case: Libya tribunal quits in Jalil row
Separately the new justice minister in Tripoli who succeeded Mustafa Abdel-Jalil, the leader of the Benghazi-based temporary government known as the Interim Transitional National Council, also addressed reporters Saturday.
Mr Abdul Jalil, a grandfatherly figure, is widely respected, but ministers in the council's executive committee, a proto-cabinet which has now relocated from Benghazi, are less immune from criticism.
Two aides to Gen Younes, Col Muhammad Khamis and Nasir al-Madhkur, were also killed in the attack, Mr Jalil said, adding that none of the bodies had been recovered.
Mr Rasmussen said he had held talks with National Transitional Council (NTC) leaders, including its chairman Mustafa Abdul Jalil, about Libya's future and the roadmap for transition to democracy.
One of the tribunal's judges, Abdullah al-Saidi, had caused controversy when he was filmed making a victory sign at the hearing at which Mr Jalil was summoned for questioning.
BBC: Abdel Fattah Younes case: Libya tribunal quits in Jalil row
The concert, to be held in at Stadium Putra Bukit Jalil on the outskirts of Kuala Lumpur, is part of Rihanna's "Good Girl Gone Bad Tour, " which began last year.
That should not surprise anyone who's been watching Mustafa Abdul Jalil, the Libyan Transitional National Council spokesman: that prominent bruise in the middle of his forehead is called a zubibah.
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