The incident is in the hands of match referee Jeff Crowe, with no immediate clarity about when a decision could be expected.
CCTV footage showed Warner apparently turning on De Kock as the players walked up a narrow staircase leading to the dressing rooms at the start of the interval in Durban in a match won by Australia.
"What was said and done during that interval was regrettable on both sides," said Australian captain Steve Smith.
"Quinton got personal and evoked an emotional response from Davey. Those things are not on from both sides. Getting personal on the field is crossing the line in my opinion."
Smith's version was disputed by South African manager Mohammed Moosajee, who blamed Warner.
"There were words said out on the field. If you are saying something you’ve got to take it and that’s the opinion of Quinton. Let the investigations begin and let the match officials decide," said Moosajee.
South African captain Faf du Plessis said the umpires needed to ensure proper behaviour on the field.
"From what I've heard there was a lot of personal stuff being said, to and from. Who started it, I don't know. If it was happening on the field it should have been nipped in the bud.
"The fact that it spilled over after the field shouldn’t have happened."
The CCTV footage shows Warner being restrained by teammates Usman Khawaja and Nathan Lyon before being persuaded to go into the dressing room by Smith.
Du Plessis said he had been aware of the incident. "I heard the commotion and went outside and just asked David to go into his dressing room. It needs to stay on the field when you are chirping each other. There need to be boundaries on that."
Smith acknowledged his players were "certainly very chirpy on the field".
But he said that as far as he aware his players had not got personal with De Kock.
Smith said he hoped the remaining three Tests would be played in the right spirit but added: "We play our best cricket when we're aggressive, when we’re in the fight together and hunting as a pack as one. We're working for each other and backing our mates up in the field. That's part of being an Australian."
He said there had been "regrettable incidents from both parties" but hoped for better behaviour in the next three Tests.
"I’m not going to say nothing will ever happen again but as far as I'm concerned we've just got to try and play within the spirit of the game."
Du Plessis said he expected aggression from the opposition when he played against Australia. "I’m certainly not sitting here complaining about it. I was disappointed to see the way it unfolded yesterday but I expect a tough series and I look forward to the battle."
According to Du Plessis, De Kock was unaffected by the incident.
"Quinny’s fine. I don’t think you get a reaction from him most of the time. When you look at him now it’s like nothing happened."
Meanwhile, Australian off-spinner Lyon was charged with conduct contrary to the spirit of the game after he dropped the ball next to AB de Villiers after completing a runout of South Africa's star batsman, an incident captured on television.
Lyon was expected to be fined or penalised with a demerit point for what is classified as a level one offence. He was said to have apologised to De Villiers and the pair were seen shaking hands while the teams warmed up on Monday.
First Published: March 6, 2018, 7:30 AM IST