The incident was earlier strongly condemned by al-Hashemi and the Association of Muslim Scholars, which represents many of Iraq's mosques.
"This heinous crime shows the hatred that the leaders and the members of the occupying force have against the Quran and the [Muslim] people," it said.
It added that it held both the US military and Iraqi government responsible for the incident.
The US army earlier said the staff sergeant, who fired bullets at the Quran and wrote graffiti inside it, had already been removed from Iraq and was to be disciplined.
A heinous crime? good grief. Personally I think that it's literally impossible to demean the Qur'an - the most anyone can do is destroy a copy, but that's an impotent gesture indeed. What need have we of apologies such as these? Why should the empty symbolism of an unbeliever concern us?
If anything is an insult to the Qur'an, it's this compulsive obsession with how the exterior of the physical book is treated rather than what's inside.
UPDATE: President Bush will also make a personal apology.