Twyford last week confirmed his office had received an email on behalf of NZ First leader Winston Peters regarding light rail on February 29 but said it was not in the public interest to reveal its contents.
RNZ has been told the email made clear NZ First's objections to the project, namely its cost and scale, as well as the potential involvement of CDPQ Infra, the Canadian partner that has a joint bid with the NZ Super Fund.
National MP Chris Bishop told RNZ that Twyford must front up and release the email.
"This is a flagship Labour Party promise. It was the first thing that Jacinda Ardern said as Labour Party leader all the way back in October 2017 and they said it would be built to Mount Roskill by 2021," Bishop said.
"But here we are in June 2020, we've got no plan, no costings, no consents, not even any idea of the route, no idea who will build it, no delivery partner and simply nothing to show for three years of work."
An agreement for "work to begin on light rail from the city to the airport in Auckland" this term was part of Labour's supply and confidence deal with the Greens.
Twyford last year conceded there would be no "spades in the ground in 2020", but said he remained confident the "multi-billion-dollar project ... to transform Auckland" would get off the ground.
There are two proposals for consideration: One from the New Zealand Transport Agency and the other from NZ Infra - the joint venture by the NZ Super Fund and the CDPQ Infra.
In late May, Twyford told reporters a proposal would go before ministers "soon" following "extensive and ongoing conversations" with NZ First.
That same day, Peters told reporters light rail was "not an issue" as it was "not going to happen in the immediate term".
"Costs have blown out massively. We've always been for heavy rail around this country ... and light rail has been suspended," Peters told reporters.
"I've made my views very clear, a long way back."
Twyford last week told Parliament it was his intention to take a proposal to Cabinet by June 19, the date at which the Government shifts into pre-election mode.
Both Peters and Twyford refused to comment to RNZ except to say the Cabinet process was underway.
Green Party transport spokesperson and associate minister for transport Julie Anne Genter also declined an interview.
Genter told Stuff last week the Green Party would campaign on light rail if the Coalition Government was unable to get it across the line.
She said the party wanted "better public transport and rapid transit for Auckland", and that specifically included light rail.
