Fifty MPs on Thursday signed a no-confidence motion against the minister, according to the official TAP news agency, after similar protests earlier in the week.
On Friday protesters chanted: "Badi get out!" and "Government of terrorism, minister of rape."
Calls for her departure have multiplied since the rape of a three-year-old girl at a children's nursery in the Tunis suburb La Marsa. The main suspect was arrested last Sunday.
Badi belongs to President Moncef Marzouki's Congress for the Republic party, Ennahda's centre-left ally in the ruling coalition, and as minister of family affairs is responsible for children's nurseries.
After reports of the rape case emerged, she said a member of the girl's family was to blame and that no measures against the nursery were needed.
"This women does not represent Tunisian women, on the contrary she has tarnished their image," Lilia Ben Kheder, a lawyer, told AFP.
"She has not fulfilled her role as minister for the affairs of women and the family, and she has done nothing to guarantee the rights of children since her appointment" in 2011, she added.
Waving shoes, a gesture considered insulting in conservative Arab societies, the protesters who gathered Friday in central Tunis also chanted: "We've had enough of the new Trabelsis."
A picture has circulated in the Tunisian media recently showing Badi holding shoes belonging to Leila Trabelsi, the loathed wife of ousted president Zine El Abidine Ben Ali, whose belongings were sold at auction late last year.
A number of people staged a counter-protest in support of the minister, shouting slogans such as: "The people still want Badi," and "Tunisia is Islamic and not secular."
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On Friday protesters chanted: "Badi get out!" and "Government of terrorism, minister of rape."
Calls for her departure have multiplied since the rape of a three-year-old girl at a children's nursery in the Tunis suburb La Marsa. The main suspect was arrested last Sunday.
Badi belongs to President Moncef Marzouki's Congress for the Republic party, Ennahda's centre-left ally in the ruling coalition, and as minister of family affairs is responsible for children's nurseries.
After reports of the rape case emerged, she said a member of the girl's family was to blame and that no measures against the nursery were needed.
"This women does not represent Tunisian women, on the contrary she has tarnished their image," Lilia Ben Kheder, a lawyer, told AFP.
"She has not fulfilled her role as minister for the affairs of women and the family, and she has done nothing to guarantee the rights of children since her appointment" in 2011, she added.
Waving shoes, a gesture considered insulting in conservative Arab societies, the protesters who gathered Friday in central Tunis also chanted: "We've had enough of the new Trabelsis."
A picture has circulated in the Tunisian media recently showing Badi holding shoes belonging to Leila Trabelsi, the loathed wife of ousted president Zine El Abidine Ben Ali, whose belongings were sold at auction late last year.
A number of people staged a counter-protest in support of the minister, shouting slogans such as: "The people still want Badi," and "Tunisia is Islamic and not secular."
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