"So I want to review that and in the meantime we are going to put a pause on that."
Last year, 5739 people were given residency under the parent category. It has ranged from 4401 to 6364 over the past decade.
Woodhouse expected the pause to be temporary and hoped to review and re-open the parent category in the middle of next year.
Prime Minister John Key said it would be a temporary measure while the criteria for the category was reviewed. "We are assessing the impacts of the costs around that on welfare and the likes, just making sure it's set in the right place."
The changes in the two-yearly review of the residency programme will also see the numbers given residency trimmed from 90,000-100,000 down to 85,000-95,000. Skilled migrants would also require more "points" to get residency than in the past.
Woodhouse also indicated changes to the numbers of people given work visas were imminent, saying he was currently reviewing the work visa scheme and expected to make changes soon.
Labour leader Andrew Little said the decision to trim numbers was a "flip flop" by National.
"It's certainly a flip flop on their part and they're doing it under pressure. Ever since the surge in immigration we've been saying there is a growing number of issues and it became apparent this year that those issues were getting acute. "
He said his main concern was that the changes did not address numbers coming on work visas.
"I'm not convinced it's actually solving the problems we know exist. We are bringing in people to do roles that the evidence suggests a lot of New Zealanders could do."
NZ First leader Winston Peters said National was clearly panicked by the polls but had not gone far enough.
"They're panicking from reading their polls. The public has serious concerns and [the Government] are tinkering around the edges."
He said even under the new numbers, an average of 1900 a week would be given residency.
Woodhouse said the changes came on the back of strong demand for residency.
Woodhouse denied it was a backdown, saying it was important to meet the balance between ensuring New Zealand attracted migrants with the skills it needed while controlling the numbers.
Key said the changes were "at the margins."
"We don't normally bang into the self-imposed cap which was 90,000 to 100,000. Because we'd done that very recently and were just going through the digestion of that, we thought it probably made sense to reduce it a small amount. It's not a dramatic move, it will have some impact."