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Property research firm CoreLogic's house price index rose 2.6 percent in December, with the average property price hitting $788,967.
That eclipses November's record, when prices grew at their fastest level in 16 years.
CoreLogic head of research Nick Goodall said the increase was driven by low interest rates, attractive capital gains and tight supply.
Judging by the growth rates, he believed jumping on the property ladder will be out of reach for more and more people in 2021.
He said scraping together enough to meet asking prices would be impossible for many, leading to outright unaffordability.
"Even with availability, credit and low interest rates, the more property [prices] increase, the more difficult it's going be for the number of people to access that amount of money to buy a property. As that happens, demand will reduce and you'll likely see a slow down in price growth," he said.
Infometrics senior economist Brad Olsen said there was increasing pressure on the government to act quickly.
"In the short term, there is going to be incredible political and economic pressure over the next six months or so around house prices, affordability and housing in general."
Olsen said this could include the Reserve Bank increasing the loan-to-value restrictions set to kick in from March, from 30 percent to 40 percent, and cracking down on investor activity.
Although increased supply was needed in the long-term, he expected the government would come in with "demand-side restrictions" in early 2021 so it could be seen to be doing something about the housing market.
According to CoreLogic, Christchurch had the smallest price increase of the main centres, inching upwards by 1.6 percent in December to $539,561.
Following the earthquakes in 2010 and 2011, the region did away with red tape to allow houses to be built faster.
Olsen said the relatively small price increase in Christchurch showed how increasing supply could help stabilise house prices and that "radical change" was needed to bring the housing crisis under control.
"Right now, the crisis is barrelling on without interruption," he said.
Meanwhile, the steepest increase of all the main centres was in Tauranga, up 6.8 percent over December to $876,122.
Accessible Properties is a national community housing provider that works with the government to provide homes for more than 3000 tenants.
She said increasing property prices weighed down the entire housing system, with the pressure pushed down through the housing continuum - home ownership, rental, affordable rental, and social housing where the demand was the greatest.
She said speeding up the construction of social houses was the only way to resolve the housing crisis.
Labour List MP Jan Tinetti, based in Tauranga, said there was work to do to increase supply, but local councils were working on this while the government was rejigging the resource consent process to allow higher density housing in the CBD.
She said the Tauranga City Council was doing a good job tackling homelessness by focusing on the public housing supply, which freed up houses for would-be buyers.