That estimate was now being considered "conservative" and said the 48,200 to 105,500 number of homes expected to be built as a result of the bill would be in addition to the 72,000 homes already expected under the Government's current density policy.
Collins claimed a victory for National.
"In January, I wrote to the Prime Minister proposing that National and Labour work on a bipartisan and urgent solution to the housing crisis," the National leader said.
"As I said then, our resource consent process makes it too difficult to build more housing in New Zealand."
Collins said that in April, she "presented a draft Bill that would have required local authorities to zone more space for new housing, drastically cutting consent requirements for those wishing to build new dwellings whether through intensification or greenfields development".
And by June, Parker and Woods wrote to National confirming "they saw merit in my proposal to increase the supply of residential housing".
"They welcomed National's contribution to further development of policy to allow a serious uplift in new housing in urban areas," she said.
National's housing spokeswoman Nicola Willis said the bill would enhance property owners' "Right to Build", making it easier for people who currently own land to build more houses on existing sections.
"This legislation takes power away from town planners and gives it back to the people they serve. It will allow our cities to develop and grow, with a range of housing types to suit people at different stages of life," she said.
Parker said that new "medium density residential standards (MDRS) will enable landowners to build up to three homes of up to three storeys on most sites up to 50% maximum coverage of the site without the need for a resource consent.
"Before this change, district plans would typically only allow for one home of up to two storeys," he said.
The bill will bring forward parts of the National Policy Statement on Urban Development - a 2019 measure to increase housing supply in cities. While widely applauded, the NPS-UD as it is known, was criticised for being too slow to take effect, with most measures coming into force in 2024.
That will now be brought forward by at least one year - something National had been urging the Government to do since December last year
Parker said that by speeding up the implementation of the NPS-UD, "councils in greater Auckland, Hamilton, Tauranga, Wellington and Christchurch have their intensification policies and rules in place by August 2023, at least a year earlier than under current timelines".
There would be some exemptions to the medium density rules, "in areas where intensification is inappropriate, such as where there is a high risk of natural hazards, or a site has heritage value".
Today 's announcement is significant as it ends decades of standoff on the housing crisis.