Ms Badenoch has denied the claims, calling them “completely false”, but he continues to stand by them.
Speaking to BBC Radio 4’s Farming Today, Rishi Sunak said Ms Badenoch had “made a fulsome statement”.
The PM was asked whether he could categorically deny Mr Staunton’s claim that a senior civil servant had told him to “stall” on compensation payments, to allow the government to “limp into the election”, apparently to help state finances.
He did not answer the question directly, but insisted that the business secretary gave a “very clear explanation”.
“Kemi made a fulsome statement about this in Parliament,” he responded. “She was right to do so and gave, I think, a very clear explanation of everything that’s happened.”
Hundreds of sub-postmasters were prosecuted because of glitches in the Horizon IT system between 1999 and 2015 in what has been called the biggest miscarriage of justice in UK history.
The government has promised to quash convictions and pay compensation, but concerns have been raised over the speed and complexity in victims securing financial redress, with just 33 claims fully settled.
The row between Ms Badenoch and Mr Staunton started when Mr Staunton told the Sunday Times that Ms Badenoch had said “someone’s got to take the rap” during his sacking last month, and that a senior civil servant had instructed the rate of payments to be slowed.
But, speaking in Parliament on Monday, Ms Badenoch furiously rejected the claims, which she labelled “a blatant attempt to seek revenge following dismissal”, adding Mr Staunton should provide evidence.
In response, a statement from Mr Staunton stated that he stood by the comment and that he had “recorded at the time in a file note which he emailed to himself and to colleagues and which is therefore traceable on the Post Office server”.
The statement added: “Mr Staunton is not in the habit of resorting to fabrication or invention and decided to go public out of a desire to ensure that the public were fully aware of the facts surrounding the multiple failures that have led to postmasters in this country being badly let down.”
The prime minister was speaking to Radio 4’s Farming Today in an exclusive interview, which will be broadcast on Wednesday morning.
