In addition to the failed hit on Malala, Fazlullah was credited with ordering a massacre of scores of pupils attending an army school in Peshawar, Pakistan.
The girls education activist said she that if it had been up to her, she would never have left.
Nasir Mahmood was killed in the lawless border region between Afghanistan and Pakistan.
The military carried out large strikes against opium production hubs in northern Helmand on Sunday.
The couple wants Taliban leaders to be tried for war crimes after their release.
The U.S. suffers the highest rate of lone-actor attacks among developed nations, a report has found.
"There are, we believe, moderate voices among the Taliban," he said.
The militant group says it would prefer that women learned how to use grenades.
The militant was also the cousin of the leader of the Pakistani Taliban, which ordered the attack on Malala.
Nearly 90,000 Rohingya have sought refuge in Bangladesh in the past 10 days, fleeing the violence.
Almost half of the four million Syrian children displaced in and around the country are not in school.
The Nobel Prize winner said the Republican frontrunner's comments were "full of hatred."
Eight days off from war and weapons could put every child in school, she says.
The 17-year-old waited for the end of her school day before responding to news of winning the Nobel Peace Prize award.
Pakistani Teen Malala Yousafzai Wins Nobel Peace Prize Along With Indian Human Rights Activist Kailash Satyarthi
Pakistani teenager Malala Yousafzai and Indian children's right activist Kailash Satyarthi have been awarded the 2014 Nobel Peace Prize