Libya's new interim leaders, the National Transitional Council, say they will hold elections and build a democratic society, which though based on Islamic law, or sharia, will respect the religious beliefs of others.
On the eve of the 10th anniversary of the September 11 terror attacks in the US by Al Qaeda, Mustafa Abdel Jalil, the council's chairman, used his first public Tripoli speech to reassure Western leaders who fear Libya may become a bastion of Islamic extemism.
"We seek a state of law, prosperity and one where sharia is the main source for legislation, and this requires many things and conditions," he said, adding that "extremist ideology" would not be tolerated.
"Ninety percent of us are moderate Muslims ... five percent are on the right and left sides," Jalil added.
He urged unity and asked those with more marginal views on religion to restrict their sparring to debate.
Many abroad point to the surge of violent Islamists in Iraq after the U.S.-led invasion and fall of Saddam Hussein in 2003, but so far, Islam appears likely to have a more benign influence in Libya.
Long oppressed Islamic groups and institutions are quietly renewing themselves and swelling their ranks, but they say they have little political ambition for now, and are more interested in furthering national unity and Islamic values.
"We don't want power or position or politics," said Mohammed Hammadi, a heavily bearded Salafist, a sect whose adherents follow what they see as a purer form of Islam as practiced by the Prophet Mohammad in the seventh century.
"Look, if you're going to drink, drink at home, don't let it affect us," said Mustapha al-Kikili, another bearded Salafist standing outside a Tripoli mosque.
Jalil said the exact place of sharia in the legal system in practice will only be settled once a new constitution is written by a constituent assembly and approved by a referendum, steps that are many months away.
Several other Arab states' laws are technically based on sharia, but the extent to which it is applied varies widely.
One Islamist who does have political ambitions is Alamin Belhaj, a member of the NTC and a senior member of Libya's Muslim Brotherhood, an Islamist group inspired by the powerful Egyptian group of the same name.
"Of course I've read a lot about the concerns of the West, but I can assure you that the Islamists in Libya, mostly or 100 percent are moderate," he said.
"Our belief is in a democratic state, in all the democratic mechanisms. We need to base our democracy on sharia," he added.
"There is nothing to fear, we are not al Qaeda, I have never been in it, I can say that with complete tranquility."
Libya's Brotherhood has fewer than 1,000 members because under Qaddafi recruitment was secretive and restricted to elites, Belhaj said. however, membership has doubled in size since the February revolt against Qaddafi's rule, he added.
But security officials in the West say they see glimmers of Al Qaeda in Libya, where they say scores of rebel fighters are associated with Al Qaeda – and where Qaddafi’s arms keep popping up in the hands of Hamas, Hizbullah, and other terror groups in the region.