Accusations of unfair play by Australia in their Test defeat by India are "outrageous", says Cricket Australia chief executive James Sutherland.
Australia skipper Steve Smith was seen looking up to his side's dressing room when pondering whether to ask for a review after he was given out lbw.
India captain Virat Kohli said Smith had "crossed the line".
The International Cricket Council confirmed no action would be taken against either captain.
Sutherland said of Smith: "We have every faith there was no ill-intent in his actions. Steve's an outstanding person."
Smith, 27, admitted his error and described it as "a bit of brain-fade".
The laws of the game forbid players from consulting with anyone off the field about whether to use the Decision Review System (DRS), given that support staff have access to television replays in the dressing room.
Kohli, 28, said it was not an isolated incident and alleges he saw Australian players looking to the dressing room for DRS assistance on two other occasions while he was batting.
"I pointed that out to the umpire as well that I had seen their players looking upstairs for confirmation," Kohli added.
"We observed that, we told the match referee and the umpire that it's been happening for the last three days and it has to stop."
However, Sutherland replied: "I find the allegations questioning the integrity of Steve Smith, the Australian team and the dressing room, outrageous.
"We reject any commentary that suggests our integrity was brought into disrepute or that systemic unfair tactics are used, and stand by Steve and the Australian cricketers who are proudly representing our country."
The Indian cricket authorities responded with a strong rebuttal, insisting they "steadfastly stand" with Kohli and his team.
"Virat Kohli is a mature and seasoned cricketer and his conduct on the field has been exemplary," said the the Board of Control for Cricket in India (BCCI).
"BCCI has requested the ICC to take cognisance of the fact that Smith admitted to a 'brain fade' at that moment.
BCCI sincerely hopes that the rest of the matches are played in the true spirit of cricket."
India's victory levelled the four-match series at 1-1 and the penultimate Test begins in Ranchi on 16 March.
Meanwhile, all-rounder Mitchell Marsh will return home from the tour of India with a shoulder injury and a replacement is expected to be announced in due course.
The reaction in Australia
A headline in The Sydney Morning Herald read: "Kohli all but accuses Australia of cheating after epic Indian Test win".
And Andrew Wu wrote that the series has become a "no-holds barred, bare-knuckle fight after a spiteful finish to the second Test".
"Relations between the two sides are now at its lowest point since the Monkeygate scandal of 2007-08", he adds, referring to an incident when India's Harbhajan Singh was accused of a racial slur aimed at Andrew Symonds. He was later exonerated.
Writing in The Age, Greg Baum says the DRS has been a "nightmare" for everyone.
"Now it [DRS] has become Frankenstein, a man-made mechanical monster. If more sensible protocols cannot be developed, it should be scrapped altogether", he says.
A headline in the Herald Sun described the Indian captain as the "cricket's ultimate bully" while The Australian says "Cricket war of words flares again".
The report in The Australian said: "Cricket Australia chief launches an extraordinary attack on Indian skipper Virat Kohli, as strained relations explode again".
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