Requiring people to ballot for Kiwibuild homes would help to ensure those on lower incomes still have a good chance, Housing Minister Phil Twyford says.
To be eligible, buyers must be purchasing their first home, or be "second chancers" - those people who have not yet had an opportunity to own their own home or who no longer own one.
They must be New Zealand citizens, permanent residents or those who ordinarily reside in New Zealand, and intend to own and live in the house for at least three years.
As of early evening there have been nearly 6000 registrations of interest in KiwiBuild since it opened online at 10am, and the numbers are climbing.
The balloting system would help to avoid those on the higher incomes blocking out those earning less, Mr Twyford said.
"Everyone has an equal shot in the ballot so people who are on a low income, or a high income, as long as they fit the criteria ... then they can have a crack at doing this."
He defended the high threshold for the income cap saying there were "not many" houses in Auckland people earning more than $100,000 could afford.
"Only five percent of builds are in that lower quartile range that first home buyers, even on quite good salaries could afford to buy, we've set the price cap so the eligible group would include 92 percent of first home buyers."
People earning between $100-$150,000 have been those hit hardest in the home ownership stakes, Mr Twyford said.
Owners would have to live in the house for at least three years - but could have paying flatmates.
The public would expect Kiwibuild homeowners to live in the house, not rent it out, he said.
"But on the other hand, people have bought these homes ... so we didn't want to put in place anything too onerous or too heavy handed."
The government would monitor whether people were living in their homes, he said, and they would also be required to sign statutory declarations.
There would be asset testing but only for the "second chancers", said the minister.
If there were family trust involved, the government would expect the beneficiaries to be named, to avoid people hiding assets like other houses.
But National said the eligibility criteria were an admission the government's "affordable" KiwiBuild houses were out of reach for many lower and middle income families.
Finance spokesperson Amy Adams said 92 percent of first home buyers would be eligible.
"That's because he knows he will fail to deliver houses that are affordable to lower and middle income earners", she said.
"Having such a wide criteria and a ballot system to determine the lucky few to get a subsidy is unfair and will mean struggling families could miss out in favour of higher income families and people with significant cash assets."
Ms Adams also questioned whether the government would be able to hit its building targets.
"Under KiwiBuild, it is yet to deliver a single home, and it has lowered its target for the first year from 10,000 homes to just 1000."
This week marks the official start of the KiwiBuild programme - where homes built under the scheme will count towards the government's target.