A migrant family who missed out on a Christmas reunion in New Zealand because of immigration visa delays will likely be getting a New Year reunion instead.

Roy Chowdhury, 42, of West Auckland, has been planning the reunion of four family members from America, Canada and India - but one did not get his visa on time despite having lodged his application in October.

Immigration New Zealand is struggling to cope with a visa application surge over the holiday season - but is granting a limited purpose visa for the last family member to visit the family here, Chowdhury said.

"We were ecstatic with this news and it's the best gift we could get this Christmas, it was really a Christmas miracle for our family."

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Chowdhury said his relative received a call from an INZ official in India the day the Herald report appeared on December 21, 2018.

But after responding to questions and sending additional supporting documents, he received a letter declining his visitor visa application.

Chowdhury wrote a strongly worded letter objecting the decision, and offered to post a $30,000 bond.

On Christmas Eve, Chowdhury was contacted by INZ assistant general manager Jeannie Melville, who he said took personal ownership of the matter.

"She was an absolute angel and I cannot even find words to express our gratitude for taking ownership to resolve this very stressful situation for us," said Chowdhury.

"She worked on her holiday and spoke to the INZ officer in India to work out a solution to this issue."

They received confirmation later that day from Melville that a limited purpose visa had been granted and the relative could join the family for a reunion and a planned South Island trip.

Subho Bose, a teacher and community worker in India, who is the partner of Chowdhury's sister, will arrive in Auckland on Friday, December 28.

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Melville confirmed that Bose has accepted the offer of a limited visa.

"The limited visa was approved on 24 December for the express purpose of a family reunion after further information was provided by Mr Bose following the decline of his original visitor visa application," Melville said.

The visa expires on January 31, 2019.

INZ is experiencing a spike in temporary visa applications, with close to 45,000 currently being processed.

There has also been a surge in the number of calls and emails to the agency, hitting 174,985 last month - a 44 per cent increase on the same time last year.

Immigration manager Michael Carley said INZ had processed 850,000 visa applications involving 1.1 million people in the 2017/18 year.

He said 75 per cent of visitor visas were approved within 18 days, but those which required additional information or verification took longer.

"Due to the high volumes currently being received, we strongly recommend applicants submit their application as early as possible prior to their intended travel date," Carley said.

Applicants are encouraged to use the Immigration Online system via the INZ website.

"It's faster and easier to apply online," Carley said.

"Applicants can upload supporting documents and photographs and pay for their application online."