The Prime Minister is urging people in unhealthy state homes to approach government agencies for help.
But the Labour Party said Housing New Zealand did not have the money to upgrade enough houses to ensure their tenants were not living in poor conditions.
John Key was responding to Radio New Zealand reports that Otara residents had spoken out about the condition of their state houses, with one family describing theirs as a "ticking time bomb" with rotten, wet flooring.
Mr Key conceded it was a problem around the country, particularly as the weather had turned cold and damp.
"We want to make sure people get assistance. I mean I accept that there's a lot of people and the Government's record actually of improving those houses (has) been a strong one over the course of the last four or five years.
"We've worked hard on trying to improve them. But I accept that some people are cold and some people have, you know, less resources and on the back of that they should definitely reach out for more help," he said.
The Minister Responsible for Housing New Zealand, Bill English, said he expected the agency to act quickly to help tenants in unhealthy homes but that it had already done a lot of work on state houses.
"Housing New Zealand has spent a lot of time and money on upgrading their stock from what was a pretty poor state six or eight years ago, hundreds of millions, and they need to keep doing that.
"Tenants, how tenants, you know, use their heating also has an effect. But where ... there is real health issues then the public agencies should be, you know, taking action," Mr English said.
Labour's housing spokesperson Phil Twyford said he was pleased the Government believed agencies should react quickly when tenants raised concerns about the state of their homes but he questioned whether they could.
"Housing New Zealand should respond quickly and move these people and fix up these houses.
"But actually the Government has run Housing New Zealand down so badly it simply doesn't have the capacity to put people into safe, warm, dry homes," Mr Twyford said.
The Green Party's co-leader Metiria Turei had no confidence the Government would make the lives of people living in unhealthy homes any better.
"I am not at all convinced by either Bill English or John Key.
"Families have been telling these agencies for years that the houses are unsuitable, their kids are sick and they urgently need to move and they're still locked in those same cold, damp houses.
"That is why kids and parents are sick and in some cases dying because there is no response," Mrs Turei said.
Meanwhile, Mr Twyford said, as bad as the problems were in state houses, it was much worse for people who rented off private landlords.
"There are far more people who are living in acute poverty in unhealthy homes in the private rental sector than there are in state housing.
"It's a much bigger problem and yet for seven years this Government has refused to do anything about putting in place minimum standards to make sure that rental properties are warm and dry."
Mr Twyford said the Government had to do more to improve the quality of both state and private rental housing.