Jacinda Ardern is admitting homelessness cannot be solved by the Government in two years, but is confident "good inroads" have been made.
The Prime Minister said every New Zealander should have a "warm, dry home", but admitted there are a "range of complex issues we have to overcome to meet those housing needs".
Ardern will attend a ceremony on Friday in Auckland to celebrate the opening of 30 two-bedroom units in south Auckland for emergency housing.
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The Monte Cecilia Housing Trust has built the fully-furnished units and its new offices on the site of an old rest home in Mangere, at a cost of $12.5 million.
Ahead of its opening, Ardern said ending homelessness in New Zealand has been a priority for her Government, and said her goal is to reach 6400 new public homes.
"We've funded and maintained over 2800 transitional housing places... our goal is to reach 6400 new public homes built."
Budget 2019 provides $283 million to fund more than 2800 transitional housing places throughout New Zealand and increase the supply of long-term transitional housing places in areas of highest need.
Ardern also pointed to the Government's announcement in August that $54 million had been allocated to support initiatives that help at-risk people and families to stay in their existing tenancies.
She then highlighted the $197 million boost in Budget 2019 to strengthen the Housing First programme, including new spending to help homeless people into permanent homes.
"There are complex issues, we're building houses as quickly as we can, but there is absolutely more that needs to be done, but we are making very good progress."
Homelessness in New Zealand has been highlighted as the worst in the OECD.
The current number of homeless people in New Zealand is currently being calculated by Stats NZ, but data from the 2013 Census put the number at around 41,000.
National's social housing spokesperson Simon O'Connor isn't convinced the Government is making a difference.
"It's unbelievable that the Prime Minister is claiming progress on housing when this Government has seen rents rise faster than any time in our history - up by an average of $50 per week," O'Connor told Newshub.
He noted the increasing waiting list for social housing, which as of May, was 11,067 - an increase of three percent on the previous quarter.
"This Government also removed tenancy reviews, which keeps people in state housing after they no longer need it, and spent $2 billion on a failed KiwiBuild project."
The Government's flagship KiwiBuild programme has been highly criticised after its promise of 1000 homes in the first year fell way off the mark, with just 258 houses built as of last month.
"I do absolutely accept there is more to do," Ardern said. "That hasn't stopped us getting on with it, but it is going to take us some time to resolve.
"It is complex and it's not just complex in terms of building the physical houses, but the reason that people find themselves homeless or in need of housing, they're complex issues too."
She said changes made to KiwiBuild in the reset, including setting aside $400 million from the $2 billion fund to support shared ownership schemes, will make a difference.
"You will have seen we announced progressive home ownerships, the next area we're moving into.
"It's all about making sure people, no matter what their circumstances, have a warm, dry, affordable home."