Footage had been released from the previous day showing a heated confrontation between Warner and de Kock outside the dressing rooms at tea on day four of the first Test.
"It's rather unfortunate that the incident took place and certainly not in the spirit of the game", he said in a Cricket South Africa statement.
Both teams were reminded by match referee Jeff Crowe of the spirit in which the game should be played. "We will await any further communication from the ICC around this incident".
David Warner's heated off-field exchange with Quinton de Kock during tea on the fourth day of the opening Test in Durban has left a bitter taste in the mouth after Australia crushed South Africa in the series opener by 118 runs.
South African television footage appeared to show Warner having to be pulled away from De Kock by Smith and Usman Khawaja.
On both occasions Cricket Australia were forced with intervene, with Warner receiving an AU$5 750 fine from CA for the Conn incident. The old days of "say what you want and do what you want", I don't think it's there anymore with the TV and stump mic.
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The skirmish started when Warner was at the centre of Australian celebrations following the run-out of AB de Villiers, however, the emotions boiled up off-field when the cricketers made their way to their respective dressing rooms. Those things are not on; you can't be getting into someone's personal life like that. "Umpires play a big role in that, to make sure you don't let it get to that stage".
After England suffered a bombardment of bouncers from Aussie speedster Mitchell Johnson in the 2013-14 Ashes, Warner climbed into Jonathan Trott, terming the South African-born batsman "pretty poor and pretty weak", and that the visitors looked like "they've got scared eyes".
But umpires Kumar Dharmasena and Sundaram Ravi ruled the light wasn't good enough for the quicks to bowl after that and Starc had to watch as spinners Nathan Lyon and Steve Smith bowled the last nine overs of the day.
Faf du Plessis said that he wasn't the one complaining. Five runs were added by the home side before Quinton de Kock (83, 149b, 11×4) was hit on the back pad and trapped leg before by Josh Hazlewood (3/61) as he tried to launch the ball over the boundary. Shortly beforehand Warner had given Markram an earful when he ran out AB de Villiers after a mix-up. If players are happy to give it, they have to be prepared to take it, too.
"We play our best cricket when we're aggressive and hunting as a pack. If I don't hear it, I'm disappointed". This was the third-highest score by a South Africa batsman in the fourth innings of a Test, and the second highest by any batsman when chasing in South Africa since their readmission. They're just like, well he's quite personal so we're going to come back at him and see how he takes it.
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