The Housing Minister says he cannot guarantee that the government will meet its target of having 1000 KiwiBuild houses built by July.
This week a report found New Zealand is one of the most unaffordable countries in the world to buy a house, with the average price more than six times the median household income.
More than six months into KiwiBuild, only 33 homes have been built - well short of the 1000 target for its first year of operation.
Mr Twyford told Morning Report it had been tougher to get the number of houses built than was expected.
"I can't guarantee that [1000 built by July this year]. I think it's going to be tough to meet that target."
"We're working flat out to meet that target. I'm not going to give you a prediction right now. We're not setting a new target."
In the early couple of years in the KiwiBuild programme the intention was to incentivise developers to build affordable, modest homes and promote buying off the plans, he said.
"The market hasn't been delivering to first-time buyers," Mr Twyford said.
"It's a matter of incentivising developers to move off the existing business model they have which is to get the maximum return on capital by building fewer but more expensive homes ... we're trying to get them to change that business model," he said.
"Currently fewer than 5 per cent of the new builds are in that bottom 25 per cent of the price range - that's where first time buyers traditionally buy."
According to the Demographia International Housing Affordability report, anything more than three times household salary is deemed unaffordable and homes more than five times median annual household income is considered severely unaffordable.
Palmerston North-Manawatu was the least expensive at 5.0, then Christchurch at 5.4, Dunedin at 6.1, Wellington at 6.3, Napier-Hastings at 6.7, Hamilton-Waikato at 6.8, then Auckland at 9.0, followed by Tauranga and the Western Bay of Plenty as the most unaffordable at 9.1.
Auckland was the seventh most unaffordable major city in the world, behind Hong Kong, Vancouver, Sydney, Melbourne, San Jose and Los Angeles.
However, Mr Twyford said if "you've got a household income of $100,000, you can afford to buy a home of $650,000".
"That's a deposit of $35,000 approximately. You can get $20,000 of that through the government's homestart subsidy.
"We're focused on building more affordable houses."
National Party leader Simon Bridges said the main driver of house prices was the lack of land for new homes.
"We've artificially constrained land," he said.
"Were the government today to come up with a comprehensive RMA [Resource Management Act] reform on both planning and the environment, we would be collaborative on that."
As for the current government's KiwiBuild policy, Mr Bridges said it had not worked.
"We're a year and a bit in, we've had 40 homes. The government said they'd do a 100,000, they're not going to meet that. I don't hold out hopes for KiwiBuild."