Asked when the reset will be revealed, Twyford said the Government had "taken the time to get this right".
"It's not just about the KiwiBuild policy, it's about the whole Government build programme. We have been working through the options but we haven't waited about to deliver a number of operational improvements.
"The future delivery of the programme is also tied up with the establishment of the new housing and urban development unit which will be the Government's delivery agency for the build programme."
He said Cabinet would shortly be considering a number of key changes to the KiwiBuild policy and its overall build programme in due course.
Speaking to media after the select committee, Twyford said the KiwiBuild was just "one slice of a very broad programme".
"We have looked at the reset as a reset of the whole Government build programme."
He would not, however, say what other areas the reset would include.
Twyford had previously said the KiwiBuild reset would be announced in June.
Asked if that was still the plan this morning, Twyford would only say: "It's going to Cabinet soon".
When pressed on what that meant for timing, he said he was not going to get into details.
National' housing spokeswoman Judith Collins said this was ridiculous.
"He has no timeframe; no timeline. It's completely unacceptable. The public has a right to know where its money is being spent.
"Phil Twyford had no answers today about what this reset is going to look like, or even any idea of what he was trying to achieve."
At the select committee, Twyford also gave an update on KiwiBuild's progress. So far, 119 KiwiBuild homes have been built with a further 400 under construction.
Twyford said 257 KiwiBuild homes are scheduled to be completed over the "coming months".
When the policy was launched, the target was for 1000 KiwiBuild homes to have been built by July this year.