Twyford's spokeswoman said a number of councils had asked for a regional fuel tax to be introduced, but there were no ongoing discussions and the tax was not being introduced.
"This is not right, this is not true, there's no discussions," she said.
Twyford also said in a statement Bridges' comments were categorically wrong.
"The Government has explicitly ruled out a regional fuel tax in Wellington," he said.
"The Wellington councils have asked for a regional fuel tax. I have ruled it out.
"Like many councils around the country, Wellington was left with a massive infrastructure deficit from the former government. These councils are desperate for funding to build much needed transport infrastructure."
On Twitter, Bridges said again that the council were talking to Government about funding their tram plan, and that a regional fuel tax was "definitely in the mix".
But Wellington Mayor Justin Lester has also come out on Twitter saying Wellington has "zero interest" in putting a fuel tax in place.
"I want to make it abundantly clear, Wellington has zero interest in implementing a fuel tax across the region. We are not discussing it with the Government," he wrote.
On Newstalk ZB this morning, Lester said a fuel tax would not be introduced under his watch.
The council has put forth proposals around the Let's Get Wellington Moving transport plan, including a range of ways to pay for it, and that was before the Government.
One potential payment method included a targeted rate for properties affected by new transport spines.
If those properties saw "exponential" growth in their value, they could be taxed on the extra growth in the form of higher rates, Lester said.
But a fuel tax was "off the table".
Greater Wellington Regional Council spokesman Stephen Heath also said there had been "no significant discussions" with the Government.
"In April this year we made a submission on the Land Transport Management (Regional Fuel Tax) Amendment Bill," he said.
The submission said that overall, Greater Wellington supported provisions to allow for the collection of a regional fuel tax.
Aside from that submission there has been no advancing of the issue, he said.