According to the report, the Taliban closed one school in Balkh province for several days after some students had their faces uncovered.
According to an official from the school, the Taliban demanded the sacking of a teacher for her "immodest" dress.
Another school now has a teacher assigned to "prevent vice and promote virtue", the HRW report said.
"The requirements on hijab are getting tougher day by day," a teacher said, adding: "They (Taliban) have spies to record and report... If students or teachers don't follow their strict hijab rules, without any discussion they fire the teachers and expel the students."
Heather Barr, associate women's rights director at the HRW, said: "The Taliban is imposing increasingly strict dress codes on both students and teachers and enforcing these dress codes by expelling students, firing teachers and even closing down the entire school.
"The students have told us they think that this is an effort by the Taliban to convince them to leave school."
Meanwhile, Rina Amiri, the US Special Representative for Human Rights and Women in Afghanistan, criticized the closing of girls' schools in Afghanistan, saying it is taking Afghanistan in a "negative direction", TOLO News reported.
"The situation of women and children is continuing to go in a very negative direction. The longer this continues in this way without robust response from the Taliban, the greater the country is going to suffer more devastating consequences," Amiri said.
But the Ministry of Education said it is ready to open girls' schools above the sixth grade if the leadership calls for it.
In addition to global reactions, the ban on girls' schooling above the sixth grade has been met with widespread reactions from politicians, civil society activists and religious scholars.
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