The controversy revolves around recent changes to immigration policy, particularly new directives governing visas, which have made it harder to bring a partner to New Zealand.
The new rules stipulate that couples must have lived together for 12 months in order to be granted a partnership visa. This change has hit the Indian diaspora hard, because of its tradition of arranged marriages.
Immigration officers were previously allowed to grant partnership visas at their discretion in exceptional cases, but new directives issued in May ended these exceptions.
Lees-Galloway said he has asked officials to review the decision.
"Whilst what Immigration New Zealand did was correct in law, it has left a lot of people worse off and I can understand the concern that people have expressed about this," he said in a video posted on Facebook on October 31.
"What I have done is asked Immigration New Zealand to look at their options and to see if we can find a fair and reasonable solution."
Indian organizations had spoken out against the changes, which they said felt like a punishment for the community.
"It's not like Kiwi culture where you live together for three, four or five years and then get married -- it doesn't work like that in India," Auckland Indian Association president Narendra Bhana told public broadcaster Radio New Zealand (RNZ) on October 23.
"I'm surprised that Immigration (NZ) has failed to understand that after all these years."
Peter Elms, national visa manager for Immigration NZ, said the move was made to prevent exceptions becoming the norm and contravening government policy.
"I don't believe this is a racist policy at all. It's a clear policy that's for all. The policies that we have in place for partnership are the policies for all non-New Zealanders," Elms told RNZ.
Controversy over the country's visa regime has been brewing for some time.
On October 23, Shane Jones, an MP for the nationalist-populist New Zealand First party and cabinet minister in the current coalition government, said people should leave the country if they don't agree with the rules.