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Waitaki Mayor Gary Kircher said the council was now starting to step back.
Further, Mr Kircher said he would be talking to Waitaki Whitestone Geopark Trust members about his present role as chairman when they met next week.
"I'm wanting to step back and it's nothing to do with the project itself other than the trust is needing to be leading this and the council will support it in whatever way we agree to support it. It's getting away from us being seen to be leading it."
He said the council was "in a phase of handing more responsibility" to the trust.
Last month, the council announced Gerald Carter, Melanie Jones, and Helen Jansen would join Mr Kircher, Mike Gray and David Higgins on the trust.
It was the sixth statement issued by council communications specialist Lisa Scott relating to the geopark since January 23.
Council economic development manager Gerard Quinn, who is also general manager of the geopark trust, said 1.1 full-time equivalent positions (FTE) had been devoted to the geopark prior to the council's submission of a 300-page dossier to Unesco headquarters in Paris in November.
Since that time just 0.3 FTE had been devoted to the bid.
The communications department had devoted 0.1 FTE to the geopark bid in recent months, Mr Quinn said.
Council departments involved in the bid included economic development; information services; heritage, environment and regulatory; communications; and people and culture.
Mr Kircher referred comment on the level of council staff commitment to the project to council chief executive Fergus Power who is on leave and could not be reached for comment.
Mr Quinn noted the trust was applying, and the council was "facilitating their application while the trust builds up its resources".
When Lincoln University researcher Dr Helen Fitt began studying the relationships between tourism operators in the district, a statement issued by the trust noted "a need for a sector representative to link the respective parties".
"People say they often don't know who to talk to; is it the geopark trust, Waitaki District Council or Tourism Waitaki? They would really like a designated person to go to with issues or questions," Dr Fitt said.