Cairns returned to New Zealand on Friday after being interviewed by London's Metropolitan Police, the ICC's anti-corruption and security unit and the England and Wales Cricket Board (ECB).
Cairns said the interview with the Metropolitan Police was in relation to an allegation that he had perjured himself at his defamation trial against Lalit Modi (Cairns v Modi) in the London High Court in 2012.
The ICC is investigating allegations of match-fixing by Cairns, Lou Vincent and Daryl Tuffey.
All three played for the Chandigarh Lions in the now-defunct Indian Cricket League.
Cairns and Tuffey have consistently denied any wrongdoing.
Reading from a prepared statement, Cairns told media at Auckland Airport that he refuted the allegations being made against him.
"Each and every allegation against me that I have cheated in cricket or attempted to induce others to cheat in cricket is false," he said.
"I have never match-fixed, sought to have others match-fix, or otherwise played the game of cricket in anything other than the spirit it so richly deserves to be played in."
The revelation that former Black Caps captains Fleming and Vettori and current New Zealand bowler Mills had assisted the ICC follows the leaking of testimonies made to the ICC by current New Zealand skipper Brendon McCullum and ex-New Zealand player Vincent to the media.
Cairns said Fleming, Vettori and Mills were people who McCullum said he had spoken to about the alleged approach.
"These three ex or current New Zealand players have made no direct accusation against me," Cairns added.
"Two of these men made statements supporting Mr McCullum's claim that he spoke to them. The third man told investigators his memory was foggy and he could not make a statement in support of Mr McCullum.
"It is also significant that none of those players seem to have spoken to anyone at the ICC or any other organisation about my alleged conversation with Mr McCullum until this year, 2014."
Cairns also said that McCullum, who testified against Cairns after allegedly being approached in 2008, had waited until February 17, 2011 to report the alleged approach.
"It is beyond doubt that regardless of what certain people have claimed recently in the media, Brendon McCullum waited three years before reporting this alleged approach to an ICC anti-corruption official," Cairns said.
"He alleges that I approached him during the ICL tournament in March 2008. It is misleading at the least for a host of people to claim that he reported my alleged corrupt approach within a timely fashion or that there had been a small delay.
"Mr McCullum first made his allegation to the ICC's ACSU on 17th February 2011. Not only was this nearly three years after the alleged approach but importantly it is 13 months before the trial in March 2012 of my case in the London High Court against Lalit Modi about match-fixing.
"At that trial every allegation that I was match-fixing was shown to be false. It is extraordinary that Mr McCullum told the ACSU in February 2011 that three years previously I approached him to match-fix yet neither he nor the ACSU anti-corruption officer who took his statement, Mr John Rhodes, took that information to the ICC or informed Mr Modi or anyone else of this startling revelation."
Cairns was also scathing about his former team-mate Vincent, who has admitted he is fully co-operating with the investigation.
"In 2008 he had a lot of problems that he has admitted to. I endeavoured to become a friend to him in these difficult times. He has betrayed the friendship I offered him," Cairns said.
"He now seeks to portray himself as a whistleblower. He is nothing of the sort. The truth is that he has been caught cheating and seeks to mitigate his sins by blaming others. The allegations he and his ex-wife make against me are despicable lies."
Cairns concluded by saying: "I find the manner in which this whole matter has progressed and the limited information that has been provided to me until very recently to be very disturbing.
"Knowing what I now know of these allegations against me I find the situation truly absurd, bizarre and scary.
"I now wait to see what happens next. Whatever happens I am hopeful that proper process will be followed and that I will be cleared of these allegations."
- Sports & Recreation
- Crime & Justice
- Lalit Modi
- London High Court
- Brendon McCullum
- New Zealand
- Metropolitan Police