The 26-year-old was roundly criticised for casting Warner as the instigator in an interview while describing himself as an impressionable rookie just wanting to 'fit in' to the team.
Bancroft said he had been in touch with Warner, and that all three banned players had supported each other.
Smith and Warner's bans for their role in trying to alter the ball in South Africa expire late next month and they are widely expected to quickly return to the national set-up.
Despite his quick exit, he was applauded by the crowd at Launceston in Tasmania as he trudged off.
Bancroft could make his comeback in Australia's Twenty20 domestic league on Sunday against the Hurricanes in Launceston.
The ruling means Smith is free to play for Comilla Victorians in the next edition of the BPL starting January 5.
Bancroft has broken his silence a week ahead of his ban running out in the form of a long letter addressed to his former self, published in the West Australian newspaper, describing his emotional journey since.
Smith is still serving a one-year ban from the international and domestic game.
Local media reported Smith was donating his fee for the advertisement to a local charity for men's mental health.
South Africa agreed not to insult Australian players regarding a ball-tampering scandal when the two teams play against each other in an upcoming one-day series.
The former Rio Tinto mining executive was only voted in for a new three-year term last week, days before a scathing independent review sparked by the cheating row slammed the governing body.
Richardson referred to the South Africa-Australia Test series when Australia captain Steve Smith, vice-captain David Warner and batsman Cameron Bancroft were slapped with lengthy bans for their roles in a plan to change the condition of the ball using sandpaper.
An emotional Warner says he realised he may never play for his country again.
Former Australia vice captain David Warner broke his silence over the ball-tampering saga on Thursday with a post on social media in which he apologised and accepted responsibility for his "part" in the scandal.
Smith and opening batsman Cameron Bancroft will return home for their role after an incident which has dragged Australian cricket's reputation through the mud.
Turnbull says that authorities needed to crack down on sledging -- verbal abuse involving players on both sides -- if it wanted cricket to "once again (be) held up as a role model".
Australia has been in turmoil after captain Steve Smith admitted on Saturday that senior players conspired with opening batsman Cameron Bancroft to tamper with the ball during the third test against South Africa in Cape Town.
There is limited social media comment and nothing from the country's cricketing heroes over the ball tampering incident.
Smith insists he will not quit after teammate Cameron Bancroft was caught using a yellow object to alter the condition of the ball on the third day of the third Test against South Africa at Newlands.
After taking the lead in the fourth Ashes Test, England head coach Trevor Bayliss rejected any ideas of ball-tampering to gain an advantage.