The Australian government would be allowed to strip Australian citizenship from the children of extremists fighting overseas under controversial legislation introduced into Parliament on Wednesday.

Details of the so-called Allegiance to Australia bill were unveiled as the mother-in-law of one man believed killed in Iraq while fighting for the Islamic State group pleaded for his wife and children to be allowed to return home.

Karen Nettleton, the mother of Khaled Sharrouf's wife, Tara, said her daughter had made the "mistake of a lifetime".