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The city has been waiting for more than a year since the Dunedin City Council submitted a bid to the Ministry of Business, Innovation and Employment - for a sum believed to be $100 million - on behalf of the project's partners.
Yesterday, Mr Cull confirmed he had written to the Government to voice his displeasure and ask "what's going on" as the delay continued.
The city had been encouraged to act quickly to get its bid in, by MBIE officials and Regional Economic Development Minister Shane Jones, and had "pulled out all the stops" to do so last year, he said.
Since then, it had "languished" with MBIE officials, although the size of the sum being sought meant it would be "ultimately a Cabinet decision".
"I am frustrated at the length of time it's taken," Mr Cull said.
Repeated attempts by the ODT to seek a meaningful update from MBIE officials had also been unsuccessful over the last year, as its staff preferred to remain tight-lipped about any progress.
Mr Cull said the delays left him worried about the impact on potential investors, from the University of Otago to private parties interested in building a hotel or apartments in the area.
"Well it can't help. We know we've got the university interested, but clearly there's a risk that if there's nothing else going to be there in the foreseeable future, the university ... they don't want to be there on their own.
"We need to have some surety that the project can actually get off the ground.
"Right from the beginning we've had interest from investors in both the hotel and the apartments and in the other buildings. Some of those investors are local and some are international. Clearly the delay would not be giving any of them any confidence."
Funding from the PGF would, if approved, pay for groundworks, building platforms and sea wall upgrades needed to prepare the site for development.
The costs of doing so had always been seen as a major impediment to development of the waterfront, meaning the PGF bid was crucial to the wider project.
A university spokeswoman declined to comment yesterday, as did MBIE staff.
A spokeswoman for Regional Economic Development Minister Shane Jones would only say ministers hoped to be in Dunedin "in the coming weeks to make some positive PGF announcements".
She would not elaborate when asked, saying Mr Jones was overseas, but Dunedin is seeking a range of PGF contributions for projects, including the planned Centre of Digital Excellence (CODE).
In July 2018, $820,000 from the PGF was granted to pay for a feasibility study and business case for the waterfront project.
At the time, Mr Jones praised the project as "iconic and transformational" for the city and unparalleled in scale in New Zealand, but also urged the parties involved to get on with it.