"Australia vice-captain David Warner and South Africa's Quinton de Kock have been reported for breaching the ICC code of conduct", cricket's governing body said in a statement.
Asked whether there would be talks between the two sides in a bid to reduce hostilities, Lehmann said: "I'm sure the coaches will chat and the captains will chat and we'll get away to play the game".
David Warner has received the emphatic backing of Australia coach Darren Lehmann, who says the opening batsman will continue as vice-captain following his spat with Quinton de Kock.
A level two offence carries three or four demerit points, while a level one offence carries one or two, meaning Warner could be banned for one Test, while the heaviest penalty De Kock faces is a fine. "Both sides are going to push the boundaries".
David Warner could be suspended from the second Test at St George's Park after he and Quinton de Kock were charged by the ICC over their heated stairwell confrontation at Kingsmead.
Aussie Test legend Shane Warne also made a public plea for both teams to move on from the tunnel tensions while condemning any form of personal attack on the cricket field.
However, reports indicate that the Australians also got personal with De Kock.
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Match referee Jeff Crowe is believed to be looking into the incident but there has been no comment yet from the International Cricket Council.
Panellist and veteran News Corp cricket writer Robert Craddock said the footage needed to be shown, as it showed Warner's true nature on the cricket field. "Chat, banter, sledging has always been a part of any series between SA & Oz".
"I don't know how their team manager [Mohammed Moosajee, who made the claims] can hear from where he's sitting". It's the way we play our cricket against them. "Have a beer together afterwards & get on with it - stop the whinging!", he said in a series of tweet.
"But Warner gets the suspension, and while he's responsible for his own actions and words, he's being allowed to do it by people above him".
Former Proteas skipper Graeme Smith also reflected his views on the incident and suggested players to draw line at personal taunts.
South African captain Faf du Plessis said the umpires needed to ensure proper behaviour on the field. "I think the less interest you take in him the better".
"Gilly - Warner crossed many personal boundaries with the South Africans, so we can't be surprised when there is eventually a reaction", he said.