Susanna Fioretti, founder of the aid organisation Nove Caring Humans, told the Italian newspaper Corriere della Sera that the girls' parents wanted their daughters to receive an education.
She said she decided to establish an underground school in Afghanistan after the Taliban returned to power and banned women from higher education.
According to Fioretti, classes were held in a room containing sewing machines. If Taliban inspectors arrived, notebooks and pens were to be hidden, and the pupils would pretend to be sewing.
She said no Taliban officials visited the premises for inspections during the first two years. After that period, she discovered that daughters of several Taliban members were also attending the school.
Asked whether there had been Taliban informants among the pupils, Fioretti replied that no, they were daughters of Taliban members. Their fathers and mothers wanted them to study.
She added that not everyone associated with the Taliban shared the same views, and that some wanted to change restrictions they considered wrong but pursued such changes discreetly.
The Italian aid worker said operating the secret school for girls involved serious risks. If someone had reported its activities to the Taliban's morality police, those involved could have faced severe consequences.
The founder of the Italian organisation also spoke about her efforts to create economic opportunities for Afghan women. She said that through dialogue and compromise with the Taliban, she had managed to establish a programme recognising Afghan women entrepreneurs.
According to Fioretti, Taliban officials were initially surprised by the proposal and asked whether she understood which country she was in. She said she explained that women's economic activities could generate income for the country to secure their approval.
Fioretti added that the Taliban eventually approved the programme, and the women who received awards attended a ceremony in the presence of a Taliban minister.
She recalled that during one meeting, a senior Taliban official asked what she, as an Italian woman, thought of the Taliban government.
Fioretti said that if she had grown up under a government like the Taliban, she would not be here today doing the work she does with this organisation.
According to her, the Taliban official responded by accusing her of having a colonial mindset but then invited her to share a meal. Fioretti said she never met the official again.