Lees-Galloway said the department had been "lawfully correct" to shift its approach to more strictly align with government policy.
But he said the change had clearly left many people, particularly Kiwi-Indians, worse off and prompted concern from community leaders and MPs.
Lees-Galloway said, as such, he'd contacted Immigration New Zealand and asked it to consider other options "as soon as possible".
"I've asked them to look at what is possible and to come back with options on how we can ensure that people who are in genuine, culturally arranged marriages have the opportunity to bring their partner to New Zealand," he said.
"We value the Kiwi-Indian community. They make an enormous contribution to our society, to our communities, and to our economy. And I am hopeful that Immigration New Zealand will be able to find a solution."
Prior to its shift in approach, Immigration NZ would grant general visitor visas to couples in arranged marriages to allow them to live together in New Zealand before applying under the partnership category.
But Lees-Galloway said he doubted officials would simply revert to that position as they felt that contravened government policy.
Asked whether the government could just change its policy or instructions, the Minister said that would take "quite some time".
"I don't think that that is what people are looking for. They're looking for a faster solution than that."
New Zealand First likely would also act as a roadblock to any formal shift in policy as its leader Winston Peters recently said his party had influenced the tougher approach.
NZ First MP Shane Jones prompted outrage last month when he said Indian activists could "catch the next flight home" if they were not happy with the country's immigration rules.
Lees-Galloway declined to say whether Jones' remarks were appropriate or helpful.
"I'm not responsible for Shane Jones. He has to take responsibility for his own comments. But this government absolutely values the contribution that the Kiwi-Indian community makes to New Zealand."
- RNZ