"We don't want the next generation to be stuck in traffic gridlock.
"We want people to be able to get home at the end of the day to their families safe, and quickly," he said.
"We know to do those things - to build a modern transport system and to make housing more affordable, we've got to do things differently."
Twyford said they also discussed formalising a partnership between central government and the Bay's local governments.
He said they talked about the "changes in direction" that might be needed when looking at the region's transport options for the future.
It was important to look towards the future when having these discussions, he said.
This meant that while they had discussed individual projects such as State Highway 2 out by Katikati, it was about looking at the bigger picture.
"We're going to lift the conversation above arguing about individual projects, to talking about 'what does the whole region need?' in terms of transport networks over the next 30 years," Twyford said.
"We're still going build roads, but we're going to broaden the conversation," he said.
Twyford also mentioned they had discussed rezoning areas of Tauranga, to "allow the city to grow up and out", and to encourage more homes to be built.
Powell said a key part of this was working with mana whenua.
"There's not anything that we can't do without having a partnership with iwi," he said.
Mana whenua representative Buddy Mikaere (Ngati Pukenga, Ngati Ranginui) said from a Māori perspective, improving the transport system in Tauranga was "critical".
"All our Māori communities live on the fringes of the city," he said.
"So transport is quite important to us, and of course the housing needs ... so this is an opportunity to reset that as well."
Twyford said he was optimistic, as Transport Minister, about the relationship between the NZ Transport Agency and local government.
"We've reset the relationship, and that's very positive," he said.
Powell agreed.
He and Twyford had met "a month ago" and started the reset process of the relationship between central and local government, he said.
This meant he, Leeder, Webber and Twyford now had a very good opportunity to move forward, Powell said.
"We've got the opportunity, because we're not big like Auckland, to really do something thinking outside the square," Webber said.
"It's not just NZTA," he said.
"It's the whole grouping of education, transport, housing and health - how do we work together, collectively ... as a legacy for generations 50 years out."