Island resident Don Wills said he saw no point in an apology.
"It doesn't matter to me because it should not have ever happened ... how can you apologise for something that shouldn't have happened?''
The exclusion zone that stretched two nautical miles, or 3.7km, around the wreck was
continuing to deprive islanders of a long-cherished fishing area.
"It's also a wonderful diving spot, it's where my son loves snorkelling, but we can't go there. You only have to go out fishing 100m and you're looking right at it. I'd rather they just focus on getting it off.''
But Tauranga Mayor Stuart Crosby, who on Monday met with Mr Zacharatos and a representative of the ship's insurance company, The Swedish Club, said he had been assured the company was committed to removing the wreckage.
The Swedish Club had spent more than $200 million on the salvage and clean-up operation and more than $70 million had been spent locally.
The company is finalising the tender process for the last phase of the salvage - the removal - and Mr Crosby was told an announcement would be made soon.
"They are here to formally apologise to communities that have been affected, to get ongoing and direct engagement with the community, and to make a commitment to make right the consequences of the grounding in its totality. In my view, that was genuine.''
Mr Zacharatos' visit also included meeting iwi in Tauranga and on Matakana Island, Western Bay of Plenty Mayor Ross Paterson and members of Bay of Plenty Regional
Council.
In a statement, Mr Zacharatos said he wished to "personally convey our deepest regret that such an event occurred''.
"I sincerely and unreservedly apologise for the actions of our staff and the damage caused.''
The ship's captain, Mauro Balomaga, and navigational officer Leonil Relon were sentenced in May and are serving seven-month prison terms.
The Daina Shipping Company is meanwhile being prosecuted by the Crown under the Resource Management Act, while affected businesses are looking at bringing their own class action - a lawsuit that be New Zealand's largest environmental claim.