The party's housing spokesperson Carál Ni Chuilin MLA hit out after an Audit Office report revealed there has been a 32% increase in the number of households designated as statutory homeless over the last five years.
She also accused the NIHE of being unable to produce first hand evidence or published statistics to show why the rate of homelessness is so high.
She said: "Whilst the report voices a concern about the possible abuse of the Housing Selection Scheme it also needs to take account of a recent UN report which highlighted the impact of unequal access to social housing behind the high proportion of Catholic households on the waiting list and registered as statutory homeless.
"As we have seen all to recently sectarian hostility and unionist territorial claims restricts access to social housing at the same time as there is a growing nationalist population with greater need to establish new households. This is leading to increasing overcrowding in many nationalist areas, with two and even three generations forced to share a home. "Sometimes homelessness is the result of personal difficulty or tragedy, family breakdown, ill health or addiction.
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"More often homelessness is the result of structural disadvantage, poor wages and high housing costs, negative equity and rising mortgage payments, unequal access to social housing, the negative impact of benefit cuts and changes.
"Everyone should have a right to a home and there is a particular emphasis on the Housing Executive to address what the Audit Office report has identified and which many of us have been pointing out for years, we need to build more social homes."
Green Party MLA Clare Bailey described the report as "damning".
She said: "In 2005, land was set aside in the Gasworks site to address the massive housing need in the Market community. For 12 years, they have been waiting for these homes to be built. Then in August 2017, the council's planning committee voted instead to allow developers to build office blocks on that land, as recommended by the BCC Planners. The developers also plan to build an extension to the hotel and a multi storey car park, and a skyscraper.
"This land was promised to the community to provide families with a future, and not line the pockets of developers. Residents in the Market have been granted two judicial reviews on these decisions and I will do whatever I can to support and highlight their campaign.
"This is a damning report on the Northern Ireland Housing Executive and the Department of Communities who have been unable to fully demonstrate the impact of its work in reducing the homelessness crisis. I, like the report authors, want to see the first-hand evidence or published statistics to show how many households have been prevented from becoming homeless by the work of NIHE and its partners."
(CD/MH)
