Mitchell said he was first informed of concerns regarding former Deputy Commissioner Jevon McSkimming on November 6 in 2024.
Last month, Mitchell said 36 emails containing allegations about McSkimming were sent to his office but he never saw them.
A protocol in place meant police staff in Mitchell's office forwarded those emails directly Coster's office.
In an interview with TVNZ yesterday, Coster said there were ministers who knew more than they admitted, including Labour leader Chris Hipkins when he was police minister in 2022 and later Mitchell.
He disputed Mitchell was not aware of the allegations before November last year, and claimed it had been discussed "informally" between the two throughout 2024.
Mitchell told RNZ's Morning Report programme, he did not know anything about the allegations before November 6 in 2024, and he would have taken action sooner if he did.
"Had Mr Coster brought forward to me the fact that Jevon McSkimming had entered into an affair [with a woman only known as Ms Z] that involved a big age gap, a big power imbalance, that involved creating a job for this person in the police and then her butting up against the power of the state I would have done what I did on the sixth of November.
"[It's] absolute complete nonsense."
Mitchell said as McSkimming was the Deputy Commissioner at the time it would not be something he would have a "causal conversation" with Coster about.
"It's a very serious matter. I take really seriously my job about protecting people..."
Mitchell confirmed the Independent Police Conduct Authority (IPCA), informed the Public Service Commission they were assessing information in relation to McSkimming in October 2024, but said he was not given any information around the nature of it.
"The IPCA were assessing information they had on him. The PSC did absolutely the right thing, by instructing Mr Coster to come and brief me on it.
"Coster did not volunteer to come and brief me on that matter."
Mitchell said the minute he found about about Ms Z and the allegations regarding McSkimming, he started taking action immediately.
Speaking to Morning Report, Prime Minister Christopher Luxon said he had not watched the full Coster interview over the weekend.
He said he had been working all weekend and had not had time to look at it, though had read media coverage.
"Mark Mitchell has addressed those challenges and for me that matter is settled. At the heart of this is a young woman who was actually let down really badly by the police executive."
Police needed to step up their culture, integrity and standards, Luxon said.
Luxon asked whether he and other ministers had overstated the findings of the IPCA - a key point in the interview at the weekend with Coster who took issue with the use of the word "corruption" by ministers.
"The IPCA did not use the word 'corruption'," Luxon said. "But it did find a total failure of leadership at the highest level and Andrew Coster accepts that."
