Mansour Hayat, of the state committee that is coordinating the claims with a UN compensation commission, told Al-Seyassah daily in an interview all of the outstanding payments were due to the government and the oil sector.
He said individuals and companies had received a total of $18.78 billion.
Iraq is seeking forgiveness of outstanding compensation, or a reduction in the amount of annual oil revenue it has been setting aside to pay war reparations to Kuwait and other countries affected by the 1990-1991 Gulf crisis.
Baghdad argues it needs the extra cash to help fund rebuilding after the 2003 US invasion that toppled Saddam Hussein. Kuwait resumed diplomatic ties with Iraq after the invasion but has so far opposed forgiving the reparations.