Twyford said the figures showed there had been three winters in a row of "very high levels of homelessness".
"[But] this winter that we've just had was the worst of the last three," he said
It comes after the Government announced in May it would spend $100 million to tackle homelessness.
This included $63.4m to expand and provide ongoing cash to support the Housing First programme - which puts chronically homeless people into permanent housing - and $37m to be spent during the winter to urgently increase housing supply.
Twyford said these efforts had led to 1300 more households getting access to public housing than a year ago.
"In the September quarter, we increased the number of public housing tenancies by 451. We also made 244 more transitional housing places available and housed 1721 households from [the] public housing waiting list," he said.
"There are also 413 homeless people or families now in stable housing through the Housing First programme in Auckland, Christchurch and Tauranga."
Through its building programme, the Government grew the public housing stock to 66,235, up from 63,511 two years ago.
But Twyford said issues of homelessness were not likely to disappear soon.
In the last quarter, 2186 people applied for Government help because they were homeless, while 4613 sought help because they had insecure accommodation.
This was up from 1098 homeless a year ago and 2515 who had insecure accommodation.
"The call by the Prime Minister in May that our Government would do all it could to help the homeless has led to a steady stream of people coming forward, confident they will get help," he said.
"The continuing demand for public housing and other housing support shows that it's going to take a concerted effort over many years to end homelessness. The housing crisis was created over a decade and isn't going to be fixed overnight."