Three local authorities where more than 4,500 families are waiting for a home have accepted just a handful of social units on offer from Nama.
The State bad bank said it had offered city and county councils a total of 6,941 homes for use as social housing, but just 2,378 had been delivered.
In Sligo, where 801 families are on the waiting list, only four have been delivered. In Donegal, where 1,267 families await a home, just five were accepted.
In Wicklow, where 2,511 households are on the waiting list, seven have been secured.
The figures are contained in Nama's end-of-year review for 2016 and come as Fianna Fáil demanded an urgent review of local authorities which turned down Nama properties.
Last October, the Irish Independent revealed that among the reasons were concerns about the quality of accommodation being offered, the impact on the social housing mix in certain areas and, in some instances, high service charges which would arise.
Hundreds of emails exchanged between Nama, the Housing Agency and city and county councils also revealed concerns surrounding the quality of information being provided.
Separately, figures obtained by Fianna Fáil under Freedom of Information rules show that more than 1,000 homes were rejected because there was no demand.
Housing spokesman Barry Cowen said "spurious reasons" were given for declining homes on the grounds that there was an over-concentration of social housing in certain areas.
"While it is too late to reverse some of the decisions taken by local authorities in relation to these properties offered by Nama, I believe there should be a review carried out by your department, and made public, about why so many of these properties were turned down," he said in a letter to Housing Minister Simon Coveney.
Some 91,600 families are on the social housing waiting list, and Nama said in its review that it had "no role" in determining the suitability of units, which was a matter for the Housing Agency and local authorities.
The bank also revealed that it had funded delivery of 4,700 new homes between 2014 and 2016, and resolved issues in 307 unfinished housing estates.
Construction work has begun, or will shortly commence, on 2,148 homes, and another 7,300 have planning permission. In addition, applications will be lodged for another 11,000 in the next year.
Nama has committed to funding 20,000 homes by the end of 2020, if commercially viable.
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