Rape per se is not mentioned in the Quran, and as such no sanction is prescribed against this crime. However, it is mentioned in the hadiths.
What non-Muslims regard as rape is not regarded by Muslims as anything immoral or illegal since Muhammad did allowed sexual intercourse with “Malak-ul-Yameen” or ‘right-hand-possessions’. This ‘right-hand-possession’ is usually taken to mean a slave. These slaves cannot be Muslims, if taken captive in war, or purchased. However a slave who converts to Islam will still remain a slave - to prevent self-emancipation through conversion.
What Abu Sayaf is saying is that it is permissible under strict Islamic law for a Muslim to take slaves and to have sex with them. It is not considered rape in Islam.
It is only recently that slavery was outlawed in Islamic countries, as late as 1967 in Saudi Arabia, and that, too, was under pressure by Western countries. Some claim with much evidence that slavery still exists in places like Sudan. Slavery is still known in Saudi Arabia and other parts of the Middle East, though not in the open.
So one would have to say that there is Quranic justification for the Abu Sayaf claim. This is according to Sharia law:
Shafi Law 9.13
Where a child or a woman is taken captive, they become slaves by the fact that of capture, and the woman’s previous marriage is immediately annulled. Reference: 'Umdat al-Salik wa 'Uddat al-Nasik (Reliance of the Traveller and Tools of the Worshipper) by Ahmad ibn Naqib al-Misri) p. 604.
faithfreedom.org/Articles/AbulKasem50519.htm