Staunton claimed he was told to “limp into the election” to save the government money.
“It was not an anti-postmaster thing, it was just straight financials,” he told The Sunday Times.
His claims drew criticism from Kemi Badenoch, the business secretary, who said the allegations were “completely false”.
Her department then published a letter from Munby to Staunton upon his appointment as Post Office chairman which set out three objectives including “reaching settlements with claimants” in the Horizon scandal.
The new memo calls into question Badenoch’s denial of his claims.
Staunton’s meeting with Munby took place a month after he took over the Post Office role from Tim Parker in December 2022.
His memo claims he told Munby he “had been on over a dozen public company boards and not seen one with so many challenges”.
The note highlighted that the board had identified a shortfall of £160 million as of September 2022.
It said: “Sarah was sympathetic to all of the above. She understood the ‘huge commercial challenge’ and the ‘seriousness’ of the financial position. She described ‘all the options as unattractive’. However, ‘politicians do not necessarily like to confront reality’. This particularly applied when there was no obvious ‘route to profitability’.
“She said we needed to know that in the run-up to the election there was no appetite to ‘rip off the band aid’. ‘Now was not the time for dealing with long-term issues.’ We needed a plan to ‘hobble’ up to the election.”
According to the memo the meeting ended with Munby telling Staunton that Grant Shapps, who had replaced Kwasi Kwarteng as business secretary, was “nice and easy but not interested in meetings… We should expect him to be ‘pushy and demanding’.”
Munby, who is now permanent secretary at the Department for Science, Innovation and Technology, denies Staunton’s claims.