Steve Smith and David Warner will stand down as captain and vice-captain for rest of Australia's third Test match against South Africa, Cricket Australia said on Sunday as it investigates a ball-tampering scandal.

There have been growing calls for Smith to be sacked as captain after he admitted being the mastermind of a premeditated plan to change the condition of the ball on the third day of the Test in Newlands on Saturday.

“Following discussions with Steve Smith and David Warner they have agreed to stand down as captain and vice-captain respectively for the remainder of this Test match,” CA chief James Sutherland said in a statement.

Sutherland said Tim Paine would step in as acting captain for the remainder of the Test.

“This Test match needs to proceed, and in the interim, we will continue to investigate this matter with the urgency that it demands,” he added.

“Both Steve and David will take to the field today under Tim's captaincy.”

Sutherland earlier on Sunday announced an investigation into the scandal, which has plunged Australian cricket into crisis and resulted in widespread condemnation at home, including from Prime Minister Malcolm Turnbull.

CA's head of integrity Iain Roy and head of team performance Pat Howard were flying to South Africa to conduct the investigation. “All Australians, like us, want answers and we will keep you updated on our findings, as a matter of priority,” the CA head added.

Television footage had shown Smith's teammate Cameron Bancroft, 25, taking a yellow object out of his pocket while fielding in the post-lunch session and appearing to rub it on the ball. He was later charged with attempting to change the condition of the ball.

Smith, 28, has earlier said he would not quit as he felt he was still “the right person for the job”.