CA chief executive James Sutherland said they were "extremely disappointed and shocked", but added that the governing body wanted to get a clearer picture of the facts before making any decisions and for now Smith would remain captain.
"I understand that that is not necessarily the fullness of response that everyone is looking for right now. But you will appreciate that there's an element of process that needs to be undertaken here," Sutherland told reporters in Melbourne.
"We will work very hard over the next couple of days to get to the bottom of it -- to understand the big picture, to understand the detail and to be making further comment on that in due course."
Smith said after play Saturday he would not quit. "I still think I'm the right person for the job," he told reporters.
But calls were growing for the 28-year-old to stand down after he admitted he was the mastermind of the premeditated plan hatched during the lunch break.
"The leadership group knew about it. We spoke about it at lunch. I'm not proud of what happened. It's not in the spirit of the game," said Smith who took over the captaincy from Michael Clarke in 2015.
"Obviously today was a big mistake on my behalf and the leadership group's behalf as well, but I take responsibility."
Television footage showed Bancroft, 25, take a yellow object out of his pocket while fielding in the post-lunch session and appearing to rub it on the ball.
"I was in the wrong place at the wrong time. I want to be accountable for my actions," said the opening batsman.
Smith insisted that coach Darren Lehmann was not part of the conspiracy even though footage appeared to show the coach sending a message onto the field with 12th man Peter Handscomb after the first footage of the incident.
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'Premeditated move to cheat'
"The coach isn't involved. It was purely the leadership group and the players came up with this," added Smith, who is playing in the 64th Test of a career which has yielded more than 6,000 runs.
After being shown on the big screen, to boos from the crowd, Bancroft appeared to hide down his trousers what was later revealed to be yellow sticky tape used to pick up abrasive dirt from the pitch.
"I was sighted on the screen and that resulted in me shoving it down my trousers. I panicked quite a lot," said Bancroft.
The umpires took no action on the field but Bancroft said he had met with the match officials after play and faced a charge of attempting to change the condition of the ball.
"We had a discussion during the break. On myself I saw an opportunity to use some yellow tape and the granules from the rough patches of the wicket to change the condition of the ball," said Bancroft who is playing in his eighth Test.
Asked whether Australia had used similar methods in previous matches, Smith said: "You can ask questions as much as you like but I can promise you this is the first time it has happened. I've made it clear it is regrettable and we move on from this and hopefully will learn something from this."
The scandal provoked widespread condemnation by former players.
"This was a premeditated move by the Australian captain to cheat," said former England skipper Nasser Hussain.
Australian leg-spin legend Shane Warne added: "I feel a bit for Cameron Bancroft because I don't think he's taken it upon himself to do something and put it in his pocket."
The four-match series, which has been plagued by bust-ups between the two teams, is locked at 1-1 and South Africa
finished the third day in a strong position, 294 runs ahead with five wickets in hand.
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