Speaking to Turkish broadcaster Haberturk, Karzai said Afghanistan will not be a well-off country without educated women.
"We will not give up on that," he said.
Most schools in the capital Kabul have stayed shut since the Taliban captured the city just over a month ago. Taliban officials say they will not return to the fundamentalist policies - including a ban on girls receiving an education - when they last ruled Afghanistan from 1996 to 2001.
They have now promised that girls will be able to study - but only in segregated classrooms.
The Taliban promised to "work hard" on girls' high school education, appoint women to cabinet positions, while vowing to build a "positive and good" relationship with the United States.