The existing consent request was made in 2013 and remains at 106th in the queue.
Waikato-Tainui says the fast-track application was never raised with them, and it's not pleased.
The chair of Te Arataura, Tainui's executive board, Rukumoana Schaafhausen, said the council shouldn't be able to use Covid-19 as an excuse to jump the queue.
"It's not related. The water crisis is not a Covid-related event and shouldn't be included in the fast-track legislation. It does need to go through the existing process and part of that process requires working alongside iwi and other authorities."
The iwi is worried about the increasing demands on the river.
"We acknowledge the current low levels in Watercare's storage system, but don't support a short-term response that could cause long-term harm."
Under the proposed fast-track legislation, iwi would be represented on the hearing panel - but the extent of that representation is unclear.
Last month, the iwi said it was initially left out of Auckland Council's discussions with Hamilton authorities to receive its unused allocation of water from the Waikato River.
Schaafhausen said the council's effort to now circumvent the process shows it still doesn't understand Tainui's rights under its Treaty settlement.
"We've got a river settlement actually that has a higher responsibility of all the local authorities to uphold the vision and strategy that exists within that settlement. So to relegate us or to sideline us to a panel is just not good enough."
The council's current consent allows it to take 150 million litres each day, plus 15 million extra due to the drought.
An application lodged in 2013 asked for an extra 200 million litres to cater to the city's growing population.
Auckland Mayor Phil Goff said now the region is facing a major water crisis, it can't wait any longer.
"After seven years surely we deserve better consideration because this is the worst drought we've had in our city's history. This is urgent, it needs to be considered in an urgent way and I think most parties understand and accept our concern, and that concern includes Waikato-Tainui."
He said the council's economist had estimated that up to 14,000 jobs could be affected by limitations on water use.
"We can't afford that sort of disruption as we recover from the economic effects of Covid-19 rather than possibly waiting another decade to be heard."
Goff blamed the slow RMA process for holding up plans to expand.
"If we were to invest tens of millions of dollars - even getting through the planning stages - would people really have thought we were wise to invest that money without the certainty of getting the consent?"
But Roger Pikia - the co-chair of the independent Waikato River Authority - doesn't buy that excuse.
"I think it's a long bow to stretch to blame the RMA because Auckland have had ample time to plan for crises situations and I think the reality is that hasn't happened.
"At the end of the day the role of the authority is to ensure that the river is placed first."
Pikia said the authority - which is tasked with protecting and restoring the river - was also surprised by Auckland Council's sudden move.
Both the River Authority and iwi want to see greater investment in long term solutions like dam storage and better infrastructure that can handle the growing population before they support rising allocations.
Schaafhausen said: "We need [the Auckland Council] to commit to what those long-term sustainable solutions might be and until we have those conversations, I just think it's disingenuous to use the fast-track bill to do what they're doing."
The select committee will consider the application as the bill makes its way through Parliament.