In the resort yesterday, Dr Smith told the Otago Daily Times while the Queenstown Lakes District Council had exceeded its year one targets under the Housing Accords and Special Housing Areas Act "progress has been slow''.
In October 2014, the council signed a housing accord with the Government, agreeing to have 1300 more homes built within the district over three years.
It set a target of 350 sections and dwelling consents in the first year, 450 in the second and 500 in the third.
In the first year, which ended in October 2015, 557 sections and dwellings were consented.
Dr Smith, who met the council yesterday, said there was "no question'' a lot of work had been done, but he had some concerns about the length of time it was taking to recommend an SHA.
"I'm hearing quite a lot of frustration from the development community about how long it's taking. These very high prices down here are a sign that we've simply not adequately met supply.''
Dr Smith said there had been a similar issue in Christchurch, after the Canterbury earthquakes, when house prices rose by about 30% with rents increasing 20% a year between 2012 and 2014.
"By putting the foot hard on the accelerator of supply, rents ... dropped by 5%. That gives me confidence that supply is the key. This issue is around delivering that as quickly as possible.''
Part of the problem in Queenstown Lakes was the "trade-off'' the council had made to include a consultative process as part of the SHA process.
It was the only council in New Zealand that "insisted'' on consulting with the community before SHAs were recommended to the minister.
"As a consequence, there have been far fewer SHAs ... [recommended].
"That's a trade-off the council and the community needs to debate ... it will delay bringing more supply on [and] more families are going to face higher rents [until the supply is adequate].''
Dr Smith said he was criticised by the Labour opposition when the accord was first signed with the QLDC.
It asked why he was "wasting my time'' in the district because it was "only an Auckland issue''.
"Housing is equally as challenging in Queenstown [and] I'm open-minded about further initiatives the Government needs to make.''
Queenstown Lakes Mayor Vanessa van Uden said the meeting with Dr Smith had been positive.
Information about the progress the council had made with SHAs would be released to the public today.
