The move was in response to calls by the PNG Teachers Association that 13,000 schools and about two million children would be impacted if the money was not released by the government.
Alongside this measure, the government announced plans to launch an investigation, headed up by the Chief Secretary to the Government Manasupe Zurenuoc, into whether school funds were being misappropriated.
O'Neill said the investigation would focus on discovering what had happened to funds that were unaccounted for. In addition, he said a list would be compiled of all schools that did not receive allocated funds, with the balance to be paid directly by the government.
He said education was a "cornerstone policy" and one that would not be "interrupted by incompetence or mismanagement".
"Anyone who gets in the way of the delivery of free education will be moved aside and we will deliver these school fees for our families," he said.
"I have directed that all schools still awaiting their school fee subsidy will receive this money direct from the government this week.
"There is no reason for any school not to open for the new school term.
"Education is a right for all children of Papua New Guinea and our government will continue to implement reform to ensure our children can attend school regardless of their economic situation."