The reason the KiwiBuild was so far behind schedule was because the buying the plans scheme had hit a snag, he said.
"It's reliant on convincing developers to shift away from a business model which sees them building smaller numbers of medium and expensive priced houses, towards building greater numbers of affordable homes."
That had proved harder than expected, he said.
But the Government was looking at other ways to ramp up the KiwiBuild numbers, he said. He would not, however, be drawn on what this entailed.
"We will have more to say in the coming weeks about that."
But he was sticking with the Government's commitment to build 100,000 homes in 10 years.
As well as targeting 1000 KiwiBuild homes by July 2019, Twyford had previously committed to building 10,000 in 2020/21 and 12,000 every year after that until 2028.
Asked if those targets were still in place, he said he "hasn't looked at that" and would not be making statements about whether or not those targets would be met.
"Targets are targets – they're something you set out to achieve but not things you can guarantee. We're not stepping away from those targets."
National's Housing spokeswoman Judith Collins said Twyford was letting down thousands of Kiwis.
KiwiBuild's website showed just 33 homes had been completed to date with 77 being built. There had been just under 270 homes prequalified, with almost 47,000 registered expressions of interests.
"If he can't organise the delivery of 1000 houses a year, why on earth would we believe the Minister when he says he's planning on building 10,000 houses a year," Collins said.
Taxpayers' Union Executive Director Jordan Williams called on Twyford to cancel the policy while it's still relatively cheap.
"By any measure, KiwiBuild is a terrible use of taxpayer funds."
Twyford's admission comes after a report from the NZ Initiative which called KiwiBuild a "massive political and bureaucratic distraction".
It also comes just a week after the head of KiwiBuild, Stephen Barclay, resigned from the role after an employment dispute.
A spokesman for Barclay said the decision to leave KiwiBuild "was not his decision".
Asked about the resignation, Twyford again said it was an employment dispute and "there were lawyers involved".
"The reason I have been unwilling and unable to comment over the last couple of months is because it would be unwise of me to wade publically into a legal dispute where my comments would risk prejudicing the interests of either, or both parties."
He said the dispute hasn't helped KiwiBuild.
The Government allocated $2 billion over 10 years to the scheme – that money would be recycled back into the scheme as more houses were built.
