Mr Parker this week voted against an amendment to the council's draft annual plan that would offer 100 percent remission to all ratepayers with red zone properties.
Those homeowners would instead qualify for 40 percent rates remission, meaning they would still have to pay 60 percent of their rates.
The exception is properties at risk of rock falls or slips, which qualify for full rates remission.
Mr Parker told TV3's The Nation this morning that the situation was not perfect but there was an arguable difference between the different property types.
"If you've got 100 percent remission that's because you can't even go down your street, you can't get on to your property, you can't store anything there, you can't go into your house to get stuff or into the garage,'' he said.
"If you've got the 40 percent remission it's because you've got access to your property, there are things that you can do there. So there is that fundamental difference.
"But I agree, it doesn't appear to be fair on the surface of it. I think it does need more work and we're certainly going to be looking at that at the moment.''
Christchurch City councillors voted 10 to four against full rates remission.
Mr Parker said the proposal could still change.
"Like anything in a draft plan, we're going to go back and look at it. So you make a decision to get the draft out, recognise that's the basis for discussion and there may be areas that will be changed - there usually are.''
The situation has been a source of frustration for homeowners who still have to pay rates on uninhabitable houses, on top of rent.
Meanwhile, rents have increased as the number of rental properties in Christchurch falls short of demand, with reports of homelessness and overcrowding as a result.
Earthquake Recovery Minister Gerry Brownlee has denied there is a rental crisis and has said the market would sort it out.
But Mr Parker today said there were significant issues in the market and more needed to be done.
"I think there are a number of people who are in what would be for them an absolute crisis,'' he said.
"On rental accommodation my personal view is that we're going to have to intervene, we're going to have to do more. So I guess my honest answer there is I don't think they're doing enough.''
Mr Parker spoke to Mr Brownlee yesterday and raised the issue of council-owned land in the central city.
"I think we should be looking at a way to encourage some private development on that land, looking at both temporary and long-term housing.''
