A car bomb in Tessalit in Mali on Friday (see 0750 GMT) (Photo: AFP)
President Moncef Marzouki asked Larayedh of the Ennadha Party, the leading faction in the ruling coaltion, to form a Government on Friday.
Outgoing Prime Minister Hamadi Jebali resigned on Tuesday because Ennahda rejected his plan for an apolitical technocrat Cabinet to prepare for elections.
Opposition secularists accuse Larayedh of leading a Ministry of Interior which has failed to curb Islamist violence.
About 3000 demonstrators marched on Tunis' main street Habib Bourguiba raising banners hostile to the Ennahda party and Larayedh and chanting, "Larayedh out" and "The people want to bring down the regime".
Meanwhile, Larayedh has tried to assemble a new Cabinet. Fights are expected over the posts of Justice and Foreign Ministers, which independents are demanding for their preferred candidates.