KABUL—When the Taliban banned girls from going to school in the 1990s, Mullah Wakil Ahmad Muttawakil served as the regime's foreign minister.

Now, Mr. Muttawakil's daughter attends a school in Kabul—one he set up. "She is in second grade and is one of the top students in her class," he said proudly, adding that he often helps with homework.

She...