Despite ongoing discussion, the restaurant owners had been unable to reach an agreement with the landlord.
"We tabled an offer and that offer was not acceptable to him''.
"His expectation of rental levels are different to what the company directors' are.''
The company website says the restaurant has stopped trading temporarily until the matter is resolved and that the owners "have all faith that there will be a positive outcome shortly''.
However, building owner City Construction Ltd said it was already considering redeveloping the site.
Iguacu had been "battling for years'' to make rent payments since becoming tenants in 2005 and it could not continue, City Construction director John Cox said.
"It's obviously a hole. It's been a hole for a while because they haven't been paying the whole rent for some time.''
"I think they thought they would make a fortune in the Rugby World Cup, which hasn't eventuated,'' he said.
Mr Cox said the company had tried to keep the rent down to help the business meet costs and believed the rent was below market value.
Iguacu is one of an increasing number of businesses forced to close their doors - an effect of the financial squeeze being felt in the industry, according to Hospitality Association president Adam Cunningham.
In 2010, 38 hospitality businesses closed, followed by 60 last year. This year, the number has already reached 64.
"That's a reflection of a reasonably tight time,'' Mr Cunningham said.
Small businesses in particular were struggling with running costs and there was often a "lack of reality from landlords'' about market pressure, he said.
"[Rent is] one of the most significant costs outside of staff wages. Rent should sit between 6-10 per cent of turnover, otherwise you're hurting.''
The restaurant owner is expected to remove chattels from the restaurant next week.
Named after Iguacu Falls on the Argentina/Brazil border, the restaurant specialised in European cuisine including a tapas menu, and had been host to classy dinners since the 1990s.
This year it again received the NZ Beef and Lamb Hallmark of Excellence Award - one of 38 Auckland restaurants to do so.
The award represented consistency and quality across a series of categories, said Beef and Lamb New Zealand spokeswoman Jennie Dean.