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"If there is money there for that project, there should also be money there for our project," Brown told the Herald.
He said Auckland has a need to bridge the Waitemata Harbour and "that's fine", but his town of 35,000 people has a need to bridge the Ashburton River.
Last week's heavy rains and floods in Canterbury closed the 90-year-old Ashburton Bridge on SH1 for two days, effectively splitting the South Island in two. Part of the bridge slumped by 13cm.
The day after visiting Ashburton and inspecting the damage firsthand, Transport Minister Michael Wood announced plans for a brand new cycling and walking bridge across the Waitemata Harbour fully funded by the public purse.
The new bridge alongside the Auckland Harbour Bridge came as a big surprise in contrast to a 15-year wait by Ashburton for a second bridge to take local traffic off SH1.
Brown said the news created some "kickback" by locals questioning why Auckland was getting so much money and Ashburton could not get a bridge.
Asked if Auckland is getting a better deal than Ashburton, Brown said: "Auckland probably always gets a better deal than Ashburton or the South Island.
"We don't ask for much but we do ask for some things to be recognised and generally they are."
The Ashburton District Council has worked for years with the NZ Transport Agency to get a second bridge connecting Ashburton with the suburb of Tinwald across the Ashburton River.
Brown said a new bridge will separate local traffic from through traffic on SH1 and improve the connectivity between Ashburton and Tinwald.
He said the daily traffic count is about 23,000 vehicles a day, which is more than the bridge can handle. A second bridge would bring the number of vehicles down to about 15,000.
Wood is making no promises to build a new bridge across the Ashburton River.
He said Ashburton's mayor and deputy mayor "understandably" raised the issue of another bridge when he visited the town last week.
"Waka Kotahi [NZTA] is working with them and the regional council on the business case. Waka Kotahi will consider funding the project to the next stage once that's complete," Wood told the Herald.
Jo Luxton, the first Labour MP to represent Ashburton in 80 years, chose her words carefully on Auckland getting a new bridge while Ashburton wades through the bureaucratic hoops with Waka Kotahi.
She said the Government sees the Ashburton bridge as a priority and is moving as quickly as possible, adding projects such as the Auckland bridge do not have any effect on the progress of a second local bridge.
"My focus at this point is that we are doing everything possible to ensure progress is being made on a second Ashburton bridge.
"It's important that we get the business case model right ... and I understand the community's frustration in how long it has taken to get to this point."