Ziauddin Yousafzai has denied claims that the family plans to seek asylum abroad and has expressed a refusal to be intimidated by the Taliban.
"I first laughed at it, because all of our sacrifices, my personal [sacrifices] or this attack on my daughter cannot have such a cheap purpose that we would go to some other country and live the rest of our life there," Yousafzai said, speaking in Urdu on Pakistani state television, the Associated Press reported.
Malala drew the ire of the Taliban after she began blogging at age 11 for the BBC about her life living under its rule in the Swat Valley region of northwestern Pakistan and advocating for education of girls.
Although she remained anonymous at first, she began using her name after the Pakistani military pushed the Taliban out of the region in 2009.
Earlier this month, a Taliban gunman shot her while she was riding the bus home from school in the city of Mingora, also injuring two other girls in the attack. She was wounded in the head and neck and is currently being treated at a hospital in Britain where she is in stable condition, able to speak and stand up with assistance.
The Taliban has vowed a second attempt on her life if she returns to Mingora, while the Pakistani government has promised to protect Malala and her family.