Darren Lehmann and James Sutherland have vehemently rejected Virat Kohli's allegations of systematic cheating in Bangalore, with Cricket Australia's chief executive slamming them as "outrageous".
India captain Kohli claimed the visitors looked to their dressing room for guidance on whether to review decisions throughout the second Test, which is banned under the laws of the game.
The International Cricket Council (ICC) is yet to charge Kohli, Steve Smith or any player for their roles in a tense Test - or the events that followed.
Sutherland, Board of Control for Cricket in India (BCCI) boss Rahul Johri and ICC chief David Richardson all have the power to report an alleged breach of the sport's code of conduct.
In the case of transgressions outside the field of play, it needs to be submitted within four days of the incident.
"I find the allegations questioning the integrity of Steve Smith, the Australian team and the dressing room, outrageous," Sutherland said, having been in the stands at M. Chinnaswamy Stadium.
"We have every faith that there was no ill-intent in his (Smith's) actions.
"We reject any commentary that suggests our integrity was brought into disrepute or that systemic unfair tactics are used."
The BCCI released a statement on Wednesday, claiming Kohli's "conduct on the field has been exemplary", but there was no reference to Kohli's claim that Australia had been using the same tactic for the "last three days".
"BCCI sincerely hopes that the rest of the matches are played in the true spirit of cricket," it noted."
BCCI has requested the ICC to take cognisance of the fact that the Australian skipper Mr. Steve Smith ... admitted to a brain fade."
Sutherland is set to have pre-planned meetings with BCCI officials later this week.
Kohli could yet be booked for his tirade. David Warner was fined for "public criticism of, or inappropriate comment" in 2014, when he accused AB de Villiers of ball-tampering in a radio interview.
Relations between the sides have soured following the acrimonious postscript to the hosts' 75-run win that levelled the four-Test series. Not since the 'monekygate' saga of 2008 has there been so much spite on and off the field in a Border-Gavaskar battle.
The only example to emerge so far of what Kohli claimed was common practice occurred on day four, when counterpart Smith was trapped lbw. It prompted the most heated of many fiery confrontations between the skippers.
Former India captains Sourav Ganguly, Sunil Gavaskar and Kapil Dev called on the ICC to investigate Australia, while Smith's predecessor Michael Clarke suggested there may be some merit to Kohli's sensational claim.
Australia coach Lehmann was "very surprised" to hear Kohli's allegations.
"Never, ever, ever," Lehmann said, when asked if he or other support staff have communicated with players regarding whether to review.
"He has his opinion and we have ours.
"We've never done any of that."
Lehmann praised his charges for not matching Kohli's in-your-face aggression.
"Gone are the days when we used to be probably the other way, and I was part of that as an Australian side," Lehmann said.
"We've changed the way we want to play."