Reporting from Tripoli, Libya— A struggle between secular politicians and Islamists seeking to define the character of the new Libya burst into the open Tuesday, highlighting the challenge authorities face with reconciling demands repressed for decades by Moammar Kadafi that are now suddenly coming to the surface.

Even as the Transitional National Council tries to establish itself in the capital, restore Libya's oil industry and public order, and crush remaining pockets of support for Kadafi, Islamists have focused their ire on Mahmoud Jibril, a U.S.-educated political scientist who is serving as de facto prime minister.

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