Wagdy Ghoneim, an imam known for his anti-semitic sermons, was invited to Tunisia by Islamist organisations but his presence has angered some groups.
"We are in the process of filing a complaint ... against those who are using mosques to political ends," Bochra Belhaj Hmida, a lawyer, said.
"There's an attack on Tunisia's sovereignty and there is no justification for using mosques to spread hateful and seditious ideology," she said.
In a letter addressed to the authorities, the civil society group, Kolna Tounes, said the preacher's tour should be cut short.
"He has incited to hatred and violence, notably against other religions. He has advocated polygamy despite it being banned under [Tunisia's] personal status code," the group said.
"He has also abetted undermining women's physical integrity by advocating female circumcision," the letter stated.
Mr Ghoneim was invited by four little known Islamist organisations.
He was cheered by thousands at a sports venue in Tunis after he arrived on Saturday and has also delivered fiery sermons at mosques in the city of Sousse and in Mehdia, about 200 kilometres south of the capital.
"Tunisia was the first country to have its revolution and, God willing, it will be the first to implement Sharia," Mr Ghoneim told the religious radio station Zitouna yesterday.
Mr Ghoneim served as a preacher in California between 2001 and 2005 before being forced to leave, officially because he had overstayed his visa.
He has since been living mainly in Yemen and Qatar and is on a British home office list of people banned from entering the UK, for allegedly encouraging acts of terrorism.