Imposing a deadline by which Christchurch earthquake claims must be settled would disadvantage some individuals, says Earthquake Recovery Minister Gerry Brownlee.
Up to 5500 people have still not settled their claims in the five years since Canterbury's 6.3 magnitude earthquake.
In Christchurch yesterday some 1000 people protested in Cathedral Square to demand a deadline for the Earthquake Commission (EQC) and insurers to complete the claims.
Mr Brownlee told Morning Report the government had stepped in to assist when problems come up, but legislation could come at a huge cost to some individuals.
"If we were to step in, in a legislative fashion, and we were requiring that everything was settled, then that would be picking winners and losers and I think that's a little inappropriate at this point."
But Christchurch mayor Lianne Dalziel told the programme some kind of end point is needed.
"This is costing people a lot of money, but it's not just the money, it's the sheer grind.
"What we wanted was to have a deadline by which the claimant could have the right to go to mediation [with] fully qualified experts, available for free."
Mr Brownlee said most of the more than 700,000 individual claims had been successful.
People 'still carry the scars'
Ms Dalziel said today's anniversary was difficult for people still living in Christchurch and those with links to the area.
"It takes you back to that moment when really our city changed forever," she told Morning Report.
"The impact that it's had on people's lives hasn't been equal across the city. Some people who've experienced loss - they've lost a loved one - people who were dreadfully injured still carry the scars today.
A public service service is being held at midday in the city's Botanic Gardens to remember the 185 people who died in the 2011 quake.