Emergency cases include people needing visas to attend a funeral, visiting a family member who's had a serious accident and compelling humanitarian reasons such as to family of the March 15 mosque attack victims.
Melville said procedural changes were made in May to improve processing times in Mumbai.
"Steps taken include moving the processing of offshore student applications for all markets, except Vietnam and India, to Palmerston North," she said.
"This removes some of the application volumes from the Mumbai office and helps to reduce its backlogs."
As of May 10, the agency received 10,702 applications, of which 9897 were unallocated.
Despite the changes, 6179 of 9207 active applications still remained unallocated as of July 22.
"INZ acknowledges there is a backlog of applications in our Mumbai office, it reflects increased volumes in the India market across all visa types," Melville added.
Processing of all new partnership visa applications from the Mumbai office will also now be handled in Hamilton.
There are currently 57 staff processing visa applications in Mumbai, and plans are for 20 more to be recruited.
"It should be noted the Mumbai office does not just handle visa applications solely from India but also processes all visa applications from Sri Lanka, Bangladesh, Nepal and Bhutan," she said.
Rishikesh Gudimalla, who married his wife Anvershana Aravind Chatla in February, has been waiting for more than six months since they lodged a partnership visitor visa on March 5.
"Without fail I contact INZ two or three times every week, but each time they say the visa has yet to be processed," said Gudimalla, an auto mechanic at Toyota Auckland.
"Each time I talk to my wife, she is in tears and emotionally broken, and I feel so helpless. When we got married, I told her we will be together in a month or two, but now I am just at a loss on what to say."
The delays are also being blamed for an "unexpected decline" in Indian visitors which Tourism NZ said cost the sector between $30 million and $50 million over nine months to April.
Education NZ also said in a briefing document in June that the delays could cost the sector dearly, with the Institute of Technology and Polytechnics alone having lost about $33m in fees over just four months.
More than 2000 people have signed a petition calling for the immigration minister to take action over the visa delays.