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The invitation was made by pressure group Keep Lake Hawea Beautiful on learning Mr Twyford would be in Queenstown on Thursday discussing housing issues.
However, Mr Twyford's press secretary Danya Levy told the Otago Daily Times yesterday Mr Twyford was not the minister responsible.
"Special housing areas come under the delegation of Associate Housing Minister Jenny Salesa.
"The invitation from Keep Hawea Beautiful was passed on to her for this reason.
"If it was Minister Twyford's area of responsibility, of course he would make time to visit.''
Ms Levy said if the SHA was signed off by Cabinet, it would be Ms Salesa who made the recommendation to the Governor-General.
A spokesman in Ms Salesa's office said he would respond today to an ODT question about whether she was prepared to visit Lake Hawea.
The SHA is opposed by many in the lakeside town who believe there is already sufficient land available for new houses within the town boundary.
The next step in the process of establishing the SHA is for a "stakeholder deed'' to be considered by the Queenstown Lakes District Council at its meeting next Thursday.
At that point, the council can decide whether it wants to recommend the SHA to the associate minister.
Council planning and development general manager Tony Avery confirmed yesterday planning practice manager Blair Devlin - who has been negotiating the stakeholder deed with Universal Developments owner Lane Hocking - has resigned from the council but others on the council team would progress the application if approved.