Twyford spoke on behalf of Genter in her absence during Question Time today, and said: "It's the convention of Government that letters between Ministers and, indeed, letters between governing parties are not released."
But Mallard questioned this, saying: "I know that I had, as an Opposition member, regularly received copies of letters between Ministers."
After Question Time, Mallard doubled down.
"I made it clear in the House that I didn't agree with the Minister's assertion that all Minister to Minister letters were withheld as a matter of course. I think we've now agreed that's not the case."
There may be other valid reasons to withhold the letter, and Genter has previously cited the need to protect free and frank expression between Ministers.
National's transport spokesman Chris Bishop said the arguments for keeping the letter secret were spurious.
"Transport Minister Phil Twyford needs to explain his role in what is increasingly looking like a Government cover-up.
"If the Government has nothing to hide, then why is it going to so much effort to keep the public from seeing how much the Greens influenced Let's Get Wellington Moving?"
Twyford and Genter have both also referred to a letter from the Chief Ombudsman to justify not releasing the letter.
That letter said it was vitally important to protect free and frank opinions when the Government consults other political parties, but it is unclear whether this referred to consultation between Ministers or between parties.
Citing this advice suggested that Genter's letter may have been sent in her capacity as a Green MP, not as a Minister, even though she had already answered questions about it in the House in her ministerial capacity.
Mallard said he would review the answers in Parliament because it was important to have a consistent approach to documents.
"Once the House has been told it is a ministerial document, it is almost certainly not appropriate to reverse that."
He said Ministers may want to use advice from the Chief Ombudsman to back up their stances in the House, but Parliament had a separate set of standards and was not bound by that advice.