Warner and South Africa wicketkeeper-batsman Quinton de Kock were reported to the ICC following an altercation near the dressing room which was captured on CCTV during an interval in play on Sunday.
Footage of the incident showed Warner apparently having to be pulled away from De Kock by team-mates Steve Smith and Usman Khawaja.
A Level 2 offence warrants up to four demerit points being issued, which equates to an automatic suspension of one Test or two ODIs/T20I, whichever comes first. The rebuttals have further underlined the distance between the two teams over events at Kingsmead, for which the ICC has charged both Warner and de Kock with "conduct bringing the game into disrepute".
First Test Australia won by 118 runs.
David Warner has avoided suspension and copped a fine of about A$13,500 after being charged over his stairway stoush with Quinton de Kock.
"When you are bringing people's families or wives into it it's unacceptable".
The second Test of the highly competitive series begins on March 9 at St George's Park in Port Elizabeth with the visitors 1-0 up the four-match series.
The teams have been given time until tomorrow to respond to the charges. Australia have long had a reputation for attempting to unsettle opposition players with words as well as actions, but Paine says there was a line the team would not cross. The deadline for de Kock to get back with an explanation is Wednesday.
"Our stuff is the way we've always played our cricket".
"We're certainly supporting David".
Warm-up match: Australia beat South Africa A by five wickets.
"Gilly - Warner crossed many personal boundaries with the South Africans, so we can't be surprised when there is eventually a reaction", he said.