He also reiterated his Government's commitment to give a separate K100 million every year to Bougainville in Special Infrastructure Funds.
The Prime Minister announced this at the end of the Joint Supervisory Body (JSB) meeting in Arawa.
It is among nine resolutions of the JSB.
"The outstanding of K621 million in Restoration Development Grants (RDG) has been outstanding for the last 18, 19 or so years," he said.
"This JSB affirmed, without any shadow of doubt, that the K621 million - confirmed by an independent United Nations' assessment - is the actual amount owed by the PNG Government to Bougainville in as far as the 2001 Peace Agreement is concerned."
He stressed that this was different from the K100 million per year commitment by his Government in 2019 for development of key infrastructure on Bougainville.
"We will deliver (K100 million annually) from 2020 going on to 2030," he said.
The Prime Minister said money should not be seen as an issue in view of the wider perspective of Bougainville.
"There is a need to bridge the emotional divide, the spiritual divide, the social divide," he said.
"This needs to take place in a region that flourishes with enabling infrastructure to support Bougainville to go into the future.
"In that context, we make clarity on the K100 million commitment by National Government to build infrastructure, going forward until 2030.
"At the very earliest, the outstanding K621 million will be reimbursed to Bougainville."
Prime Minister Marape also said the ABG wanted a sovereign guarantee for a loan, something that Bougainville and PNG treasuries were working on.
The JSB meeting was hailed a success.
ABG President Ishmael Toroama described the JSB meeting as an "honorable moment".
He said, "At the same time, we have set tasks for ourselves, in how we can totally work together, in reaching that understanding. This is my first JSB. Today, we reached an understanding, a joint agreement. This is one of the steps forward we have taken, and that is another big challenge that is coming ahead. I'm confident that whatever happens as an outcome of the consultations, will reflect the joint efforts that we have taken together."