Cricket Australia CEO James Sutherland came out strongly in defence of Smith, who was accused of flouting the rules during Tuesday's defeat in Bangalore.
India captain Virat Kohli and others said Smith had overstepped the mark by appearing to look for a signal from the dressing-room when weighing whether to appeal his dismissal for lbw.
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"I find the allegations questioning the integrity of Steve Smith, the Australian team and the dressing room, outrageous," said Cricket Australia chief executive James Sutherland.
"Steve is an outstanding cricketer and person, and role model to many aspiring cricketers and we have every faith that there was no ill-intent in his actions.
"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."
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The rules forbid players from consulting with anyone off the field about whether to seek a review from the umpires.
After the match, Smith blamed a "brain fade", suggesting the incident was a one-off. But Kohli insisted "it's been happening for the last three days, and it has to stop".
Although no formal complaint has been laid, a source in the Indian board told AFP that the team would press for charges.
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