A social housing provider believes the Government's defence of KiwiBuild is flawed.
Concerns are being raised about the income levels needed to service a mortgage on the homes, which in Auckland cost at least $600,000 - more if you want more than two bedrooms.
Prime Minister Jacinda Ardern says the scheme isn't about bankrolling housing.
"It's not about subsidising housing, but about providing more supply in the housing market where builders and developers just were not producing houses," she told Newshub Nation on Saturday.
There has been criticism from National housing spokesperson Judith Collins the first family to move into a KiwiBuild home was a young professional couple - one a soon-to-be doctor and the other a marketing manager.
"The KiwiBuild policy is underwhelming and a disappointment to first-home buyers across the country. The Government needs to urgently review the entire scheme."
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Buyers still have to pay the full cost, and that money is put back into the KiwiBuild fund to spend on building more homes. Bernie Smith of Monte Cecilia Housing Trust says it's not good enough.
"Why is she defending it? If the Government isn't bankrolling it, why isn't there more money available for social housing, affordable rentals and more affordable first-home purchases?"
Mr Smith says the scheme is helping perpetuate the working poor.
"[They are] seeking to get onto the housing ladder, but the $600,000, $650,000 entry level is just too high for them."
Instead, he'd like to see the Government try a shared equity model - where first-home buyers get a mortgage they can afford to service, and the Government stumps up the rest. The owner later buys the rest of the home off the Government when they can afford to.
"The New Zealand public as a whole would be more than happy for them to redirect some of the KiwiBuild funding towards a shared equity home ownership at a lower entry level, looking at increasing rental supply."
Mr Twyford told Newshub the Government is looking at such a scheme.
"We understand that there are a lot of people who would love to have a crack at home ownership but simply cannot afford to take on a mortgage. That's why we are working on a shared equity scheme that will give them that chance. This work is ongoing and more details will be announced in the future."
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He said the fact a professional young couple were eligible for KiwiSaver shows "how bad the national housing crisis has become".
"The income bracket from $80,000 to around $180,000 has experienced the greatest fall in homeownership in the last decade."
The previous Labour Government launched a short-lived shared equity scheme in 2008, before being voted out of office.
Shared equity schemes are already offered by private providers, such as the NZ Housing Foundation, backed by wealthy philanthropist Stephen Tindall.