Virat Kohli called for "strict action" to be taken after India players claimed they were subjected to racial abuse by spectators during the third Test against Australia at the SCG.
Six people were ejected from the iconic Sydney venue on day four after India paceman Mohammed Siraj reported he was the target of abuse while he was fielding on the boundary.
The India team staff also reported alleged racial abuse of Jasprit Bumrah and Siraj on Saturday.
Play was halted for around 10 minutes on Sunday, with umpires and security guards holding discussions before the spectators were removed by New South Wales Police.
The International Cricket Council (ICC) strongly condemned the reported incidents and offered Cricket Australia (CA) all necessary support with an investigation.
India captain Kohli, who is back in his homeland as his wife is expecting a baby, said action must be taken as soon as possible.
He tweeted: "Racial abuse is absolutely unacceptable. Having gone through many incidents of really pathetic things said on the boundary Iines, this is the absolute peak of rowdy behaviour. It's sad to see this happen on the field.
"The incident needs to be looked at with absolute urgency and seriousness and strict action against the offenders should set things straight for once."
CA head of integrity and security Sean Carroll earlier said in a statement: "Cricket Australia condemns in the strongest terms possible all discriminatory behaviour.
"If you engage in racist abuse, you are not welcome in Australian cricket. CA is awaiting the outcome of the International Cricket Council's investigation into the matter reported at the SCG on Saturday.
"Once those responsible are identified, CA will take the strongest measures possible under our anti-harassment code, including lengthy bans, further sanctions and referral to NSW Police.
"As series hosts, we unreservedly apologise to our friends in the Indian cricket team and assure them we will prosecute the matter to its fullest extent."
India spinner Ravichandran Ashwin claimed India have experienced abuse on previous tours of Australia.
"This is my fourth tour to Australia and in Sydney, especially, we have had a few experiences even in the past," he said.
"I think one or two times even the players have reacted and got into trouble in the past, and that's not because of the player, it is actually because of the way the crowd has been speaking, especially the people close to the boundary edge.
"They have been quite nasty, they have been hurling abuse as well, but this is the time they have gone one step ahead and used racial abuse.
"There was an official complaint lodged yesterday, and the umpires also mentioned it to us that we must bring it to their notice as soon as it happens, on the field, and then they will be able to take action.
"It is definitely not acceptable in this day and age. We have seen a lot, right? We have evolved as a society. This must be definitely dealt with an iron fist. And we must make sure that it doesn't happen again."
Australia are strong favourites to take a 2-1 series lead, as India were 98-2 at stumps on the penultimate day after being set 407 to win.