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The law could affect senior members of the government, including Prime Minister Ali Zeidan.
BBC: Libya parliament bans Gaddafi-era officials
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Also on Sunday, Mr Zeidan warned that members of his government had received death threats.
BBC: Libya PM's aide Mohamed al-Ghattous 'kidnapped'
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Mr Zeidan thanked the Egyptian authorities for their "judicial co-operation" over Mr Gaddaf al-Dam.
BBC: Gaddafi cousin Ahmed Gaddaf al-Dam arrested in Egypt
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We are pleased also to welcome Libyan Prime Minister Zeidan to Washington for his first official visit.
WHITEHOUSE: Press Briefing
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Both Mr Zeidan and GNC speaker Mohamed Megaryef were diplomats before the revolution.
BBC: Libya parliament bans Gaddafi-era officials
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An aide to Libya's Prime Minister Ali Zeidan has been kidnapped on the outskirts of the capital, Tripoli, government officials say.
BBC: Libya PM's aide Mohamed al-Ghattous 'kidnapped'
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Former French President Nicolas Sarkozy, who championed the intervention, has been in Tripoli for the day, meeting Libyan Prime Minister Ali Zeidan.
BBC: Gaddafi cousin Ahmed Gaddaf al-Dam arrested in Egypt
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Prime Minister Ali Zeidan, at a news conference, urged Libyans to back their government in the face of "people who want to destabilise the country".
BBC: Libya gunmen surround Tripoli foreign ministry
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Mr Cameron announced at a joint news conference in Tripoli with his Libyan counterpart Ali Zeidan that officers from Dumfries and Galloway Constabulary had been granted permission to visit the country.
BBC: Lockerbie plane
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Zeidan ag Sidi Lamine, a former rebel now living in Bamako and part of the Malian government, said talks with the rebels were possible if it would accept the country's territorial integrity.
CNN: Islamist militants taking advantage of chaos in Mali