He added: "INZ would like to apologise for any inconvenience caused and is pleased the matter has been resolved in time for Ms Ghaemmaghami intended travel plans. INZ won't be making any further comment on this case."
Festival organisers said they were "thrilled" with the decision.
They said Ghaemmaghami was notified of the change by the New Zealand Immigration Office in London this morning.
She was "incredibly relieved", Doc Edge said, and "very thankful" for the support she received from New Zealanders and people around the world.
"Thanks to all my filmmaker friends and documentary organisations from all around the world for showing their support in regards to the visa problem," Ghaemmaghami said in a statement this morning.
"Also, thanks to New Zealand immigration system for showing a responsible and quick reaction to request of more than 1000 people," she said, referring to a petition that was set up by Doc Edge.
"I am so excited to be able to present my movie to New Zealand audiences in the prestigious Doc Edge Festival. Now I feel that I am a member of a big family of filmmakers all around the world who believe that there should not be any borders for artists."
Responding to the news, Doc Edge said: "Thanks INZ for reconsidering its decision. We also thank our wonderful caring community for the wide support over the last few days.
"We are delighted that Rokhsareh will attend Doc Edge Festival and Screen Edge Forum and encourage everyone to attend the screenings."
Ghaemmaghami is due to arrive in the country on May 12.
She was formally invited to the Doc Edge festival and its industry event, Screen Edge Forum, but her visa application was initially denied by the INZ office in Washington DC.
She received a letter saying New Zealand authorities did not believe she was a genuine visitor, Radio New Zealand reported.
The letter also said it did not recognise the Doc Edge festival or its invitation.
"They wrote a letter to me that because they are not sure that I won't stay in New Zealand forever, they can't give me a visa. They told me that I don't have enough financial and family ties in my own country," Ghaemmaghami said, according to RNZ.
She is set to be a guest speaker, hold classes, feature at question and answer sessions, and present her film.
Ghaemmaghami has been travelling around the world showcasing Sonita, including recent trips to the United States, Europe and Mexico.
She also plans to visit Canada and Australia.
SONITA (Trailer) from filmswelike on Vimeo.
Earlier this week, 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," they said.
"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."
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.
Shanan and Lee asked Mr Woodhouse to review the decision and approve Ghaemmaghami's visa as soon as possible.
They also asked that an apology be issued from INZ for the "humiliation and embarrassment" caused.
Amnesty International also added its voice to the fight.
The organisation is a sponsor of Sonita at the festival and its activism manager, Margaret Taylor, expressed concern earlier this week 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 also welcomed a reassessment of the decision.
Yesterday INZ said it was still reviewing the decision and that it would be in contact with Ghaemmaghami this week.
"INZ is aware of her intended travel dates and will ensure all aspects of the review are completed and the outcome communicated to Ms Ghaemmaghami well before these dates. INZ is unable to make any further comment until the review is completed and the outcome communicated to Ms Ghaemmaghami."
That outcome was announced this morning.
