Homeless charity Focus Ireland has said NAMA must put a greater emphasis on creating quality social housing as the agency moves towards its final stages.
NAMA has identified over 5,200 residential properties as potentially suitable for social housing of which 736 have been delivered for social housing use.
2,800 of these properties were rejected by local authorities because they were deemed unsuitable or there was no demand in the area.
Focus Ireland spokesperson Mike Allen said NAMA must concentrate on delivering substantial numbers of quality social housing units.
"The units have been turned down by local authorities as unsuitable for social housing; now that might be that they are just badly built and they would be a huge liability, or it might be that they are in areas where there is already a very high density of local authority housing and it's not appropriate to have more," Mr Allen said.
"The simple fact is that not enough homes are coming through to us from NAMA and that's an absolute fact which we would stand over and say that something should be done about," he added.
Mr Allen also welcomed the houses that NAMA has made available for social housing to date and said it makes a huge difference to the lives of families who had been homeless,
"It transforms their lives, the experience of becoming homeless is devastating for the parents, the sense of powerlessness and the dislocation for the children is appalling," he said.
"Most of the families who have become homeless never thought it would happen to them, so the access to social housing in this case from NAMA means they can start rebuilding their lives and return to the normality that we all want to have."
In a statement to RTÉ’s Morning Ireland, NAMA said most of the 14,000 residential units under the control of NAMA debtors and receivers have either been sold or are rented to tenants.
The agency said it is not open to NAMA nor would it be appropriate to de-tenant occupied units.
The statement said that while it is up to the local authorities to decide which units are suitable, there is confirmed demand for 2,000 units and demand is still being assessed for another 540 units - bringing the total number of properties that may be delivered to over 2,500.
The agency also said that when units are identified as being suitable for social housing NAMA seeks to move the process along as quickly as possible.
NAMA said that when a residential unit is incomplete but deemed suitable for social housing the agency makes funds available for its completion
People Before Profit TD Richard Boyd Barrett said the Government must change NAMA's mandate so that the emphasis is on delivering social and affordable housing:
"I think what we need is the Government to change NAMA's mandate. Instead of its mandate being to make profits from the sales of its asset portfolio, its main mandate now should be to deliver social and affordable housing for the tens of thousands of families who urgently need it and that would be done through transferring at a much faster pace assets to local authorities for social housing and using huge cash reserves it has to fund a major state led social housing programme," he commented.