But a readers' poll on the Herald website is more evenly split, showing 49 per cent of 13,300 people so far opposed to the tax, 42 per cent support it and 7 per cent say "maybe".
Gavin Logan of Avondale said: "No I will not be happy to pay this tax if it is introduced and will make sure that every time I am out of the Auckland Council area that I fill my car to the max to avoid as much of this tax as I can."
Shaun Coffee-Todd wrote: "As someone who lives in Auckland and who would be directly impacted by a regional fuel tax, I fully support it. My only caveat is that 100 per cent of revenue raised should be used to fund transport projects in greater Auckland only."
Goff said Auckland has to pay its share of desperately needed transport infrastructure to tackle congestion which is worsening with 50,000 people being added to the city each year.
"Light rail will help decongest our roads and provide a 21st century gateway to visitors to Auckland. It will also allow for more intensive housing development around transport hubs bringing economic benefits to those suburbs it travels through.
"A fuel tax is effective and cheap, and easy to administer. It will help ensure that Auckland can pay its share of the nearly $27 billion expenditure on transport infrastructure over the next 10 years.
"Without this level of investment our rapidly growing population will worsen congestion on our roads with mounting costs from frustration and lost productivity".
Goff said a regional fuel tax of 10 cents a litre would raise twice as much money as the Interim Transport Levy to invest in new transport infrastructure
The levy was an eleventh-hour addition to the 10-year budget in 2015, which is due to expire next year.
Goff, who campaigned on getting rid of the interim levy if it was replaced by a regional petrol tax, said once the petrol tax was in place the levy "would go completely".
"Transport investment in Auckland is a partnership between government and council, and I look forward to discussions with the Prime Minister and Minister for Transport in the coming weeks to begin work to introduce the fuel tax in Auckland as quickly as possible, and to agree the funding," Goff said.
Twyford, who also has the portfolios of housing and urban development and largely shaped Labour's policies for Auckland, said he would be talking with Auckland Council about the regional petrol tax to get timeframes in place.
He said one of the Government's first steps will be to sit down with council and renegotiate a joint government-council 10-year transport plan, known as the Auckland Transport Alignment Project (ATAP).
This will determine the Government and council's share of the costs and how to plug a $6b funding gap in the current ATAP budget. Last month, Twyford told the Herald the Government would pay most of the costs for trams but council would shoulder a "significant share".
"It is a major priority for us to start immediately to roll out the rapid transit system for Auckland," Twyford said.
"To do this we need to have the funding commitments in place, including the regional fuel tax."