Nandy said he was misunderstood, but Bahujan Samaj Party (BSP) leader Mayawati asked the Rajasthan government to take strong action against him, while Republican Party of India (RPI) chief Ramdas Athawale demanded that Nandy take back his comments.
There were also protests by Scheduled Caste, Scheduled Tribe and Other Backward Classes (OBC) groups outside the festival venue - the Diggi Palace.
Police said a first information report (FIR) was lodged against Nandy under the section 3(1) of the SC/ST Act, which was non-bailable and invited a 10-year jail term. The case was filed by a person identified as Ram Ratan Meena.
Festival director Sanjoy K. Roy was also booked, police said.
A police official at Jaipur's Ashok Nagar police station, where the complaint was lodged, however, told IANS that they would first investigate the incident and then decide on any action.
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Amid protests, police helped Nandy, who is in his late 70s, get out of the venue from a back door in the evening, a constable told IANS.
Addressing a press conference in the evening, Nandy told reporters he was misunderstood. "As should be clear, there was neither any intention nor any attempt to hurt any community," he said.
Roy said: "They have clarified their position and have understood that it was a misunderstanding. Controversies are easily created. Please be responsible."
However, the BSP did not accept the clarification.
Talking to media persons in Delhi, Mayawati said Nandy's comments were wrong, baseless and unfortunate.
"Our party demands that the Rajasthan government should register a case and he should be sent to jail," she said.
She said the comments reflected a casteist mindset and were made as part of a thought-out conspiracy to defame people from these communities.
Mayawati said the organisers should also immediately "throw out" Nandy from the festival for his "castiest remarks".
Asked if the party will raise the issue in budget session of parliament, she said the party will take into account the steps taken by the state government, the organisers and the "kind of apology" tendered by Nandy.
Nandy stirred a row at a morning session, titled "Republic of Ideas", when he said: "It will be an undignified and vulgar statement. But the fact is that most of the corrupt come from the OBC, the Scheduled Castes and now increasingly STs. As long as it is the case, the Indian republic will survive."
"I will give an example. The state of least corruption is West Bengal. In the last 100 years, nobody from the backward classes and the SCs and STs have come anywhere near power in West Bengal. It is an absolutely clean state," Nandy said.
At the press conference, Nandy said he meant to endorse fellow panelist Tarun Tejpal's statement that corruption in India was "an equalising force".
In a written statement, he said: "This is not what I meant or what I wanted to say. I endorsed the statement of Tarun Tejpal, editor of Tehelka, that corruption in India is an equalising force. I do believe that a zero corruption society in India will be a despotic society."
"I also said if people like me or Richard Sorabjee (one of the speakers) want to be corrupt, I shall possibly send his son to Harvard giving him a fellowship and he can send my daughter to Oxford. No one will think it to be corruption. Indeed, it will look like supporting talent."
"But when Dalits, tribals and the OBCs are corrupt, it looks very corrupt indeed," he added.
"However, this second corruption equalizes. It gives them access to their entitlements. And so, as long as this equation persists, I have hope for the republic."
Hoping this would end the matter, Nandy said he was sorry if some had misunderstood him. "As should be clear from this statement, there was neither any intention nor any attempt to hurt any community. If anyone is genuinely hurt, even if through misunderstanding, I am sorry about that, too."