He said he had "reservations" about the tax but wanted the option available as soon as possible in case the city needed it.
Revenue from a fuel tax would help the city pay for some $115 million in transport projects over the next decade that may not be eligible for funding through the National Land Transport Fund.
Brownless said that could include the long-awaited four lanes for Turret Rd.
Western Bay's council submitted against the bill.
Mayor Garry Webber said the system would be costly to run, create inequity between regions as people hopped borders for cheaper fuel, and would unfairly punish people in rural or remote areas.
"Those that travel further would pay more."
Tauranga MP Simon Bridges has also slammed Tauranga council's support for the bill, saying the city's residents did not need a fuel tax.
As Opposition leader, Bridges has said National would overturn the legislation if it was returned to power in 2020.
"The fuel tax won't make a blind bit of difference to the transport issues Tauranga has," he said.
"Some experts say petrol prices might hit $3 per litre - the Government shouldn't help that along."
Twyford said the Government had "no intention" of changing the bill to allow other regions access to petrol taxes earlier than 2021.
Auckland was prioritised because the last Government's policies left it a "transport basketcase".
Other councils including Hamilton and Christchurch had also expressed interest in taking advantage of the legislation, Twyford said.
Groups lobbying Western Bay councils for more and better transport investment have applauded Tauranga's support for the tax.
Heidi Hughes of Greater Tauranga said it a fuel tax could make people think twice about driving, as well as better apportioning costs of improving the transport network to the most expensive user category - drivers.
Tauranga Chamber of Commerce chief executive Stan Gregec said he believed the business community could support the tax, provided it was transparent and used for a specific purpose: "to contribute to relieving congestion in our city - which is affecting business big time and adding to cost anyway."
Priority One chief executive Nigel Tutt said traffic congestion was the "number one issue" for Tauranga and councils "needed to have every funding tool available to them".
"I think there would be a willingness to pay if people can see what the money goes towards."
Auckland's petrol tax plan
- Council support for 11.5c per litre.
- Could rise to 25c per litre over 3 years.
- Expected to be formally approved on May 31.
- Would come into effect on July 1.
- Estimated to raise $1.5 billion over 10 years.
Source: Auckland Council
Uber drivers
Te Puke-based Uber driver Jonathan Clayton says he can see both sides of the Regional Fuel Tax debate.
"I can see the benefit of improving the roads. But I also know how it will affect people working behind the wheel."
Higher petrol costs would make it even harder than it already was for turn a liveable profit as a driver, he said.
"I would have to consider an electric car or a hybrid."
The tax would hit inner-city drivers hardest, as they would churn through more petrol stopping and starting than people driving on open roads.
