The INZ office told her in a letter they did not believe she was a genuine visitor and did not recognise the festival or its invitation.
Amnesty International is a sponsor of Sonita at the festival and the organisation's activism manager, Margaret Taylor, this afternoon expressed concern over INZ's decision.
"Film directors are often the target of crackdowns by governments in their own countries, but it is deeply concerning to see our own country rejecting this visa application," she said.
"Rokhsareh plans to visit several other countries such as Australia, Turkey and the US on her worldwide tour to promotes this documentary, so it's surprising that New Zealand has rejected her application on the grounds that she may be a flight risk."
Amnesty International would welcome a reassessment of the decision, she said.
The festival has set up a petition calling for the decision to be reversed.
The New Zealand Herald called the Embassy of the Islamic Republic Of Iran in Wellington for comment, but there was no answer.
When contacted by the Herald this morning, INZ assistant general manager Michael Carley said the case was being reviewed by the Washington office and that a decision was expected shortly.
This morning, directors of the Doc Edge festival sent a letter to New Zealand Minister of Immigration, Michael Woodhouse, saying it was with "deep regret" that they learnt of its decision to decline Ghaemmaghami's visa.
Doc Edge's Dan Shanan and Alex Lee said they had invited Ghaemmaghami to events in Wellington and Auckland and were "disappointed" with the decision.
"There is damage done to both the reputation of the festival and New Zealand as a whole. The message going out to the world does not go hand in hand with our New Zealand hospitality and as a country which is supposed to promote and support innovations, arts and culture.
"Rokhsareh is widely followed around the world on social media and the fall out has seen international industry and key filmmakers, broadcasters, sales agents and others comment publicly that they condemn the decision and that they will not be wanting to visit New Zealand any time soon."
Shanan and Lee said no one from INZ had contacted them about Ghaemmaghami's bona fides and that a quick Google search would have established her international reputation.
She recently won the best International Feature Documentary and Audience Award at the Sundance Film Festival for Sonita, which is also a finalist in the Doc Edge Best International Film and Best International Director categories.
SONITA (Trailer) from filmswelike on Vimeo.
Shanan and Lee have asked Mr Woodhouse to review the decision and approve Ghaemmaghami's visa as soon as possible.
"We ask that an apology be issued from [INZ] Washington D.C. to Rokhsareh for the humiliation and embarrassment caused."
In relation to the festival and its invitation not being recognised, they said: "Doc Edge is an internationally respected documentary festival. We have carefully built up our festival and its reputation over ten years, it was recently selected as a qualifying festival for the Academy Awards® short documentary category."
Meanwhile, a spokeswoman for Mr Woodhouse told the Herald this morning that the minister had been in meetings and so had not yet seen the letter from the Doc Edge festival directors.
"But obviously it was a decision made by Immigration New Zealand, so at this stage it's more appropriate for Immigration New Zealand to comment on that," she said.
"I understand that they are talking with the Washington office, which is where the decision was made..."
