Kumar was supported by BJP MPs Manohar Utawal and Nand Kumar Chauhan.
An infuriated Scindia, the Congress Chief Whip in the Lok Sabha, asked the BJP members to prove their charges or else resign.
"I have recordings of that event. I challenge them to prove the charges. If they prove it, I will resign from the house or else the three MPs should resign," the Congress leader said.
Scindia said the members concerned should at least apologise.
Congress members, including Scindia, rushed towards the Speaker's podium and sought an apology from Virendra Kumar, who was present in the house.
Kumar wanted to respond but Speaker Sumitra Mahajan did not allow.
Amid the din, Congress leader Mallikarjun Kharge stood up to speak, but was denied permission by the Speaker. Kharge said his voice was being suppressed.
Kharge's remarks agitated the treasury benches and led to a heated argument with Parliamentary Affairs Minister H N Ananth Kumar.
Ananth Kumar said Kharge's remarks were against the Chair and this cannot be tolerated.
Mahajan said she had allowed Scindia to speak, but he rushed towards the Speaker's podium with other Congress members.
"If you come towards the podium every now and then, how will the house function? You will have to understand this. If you don't want the house to function, tell me in advance. I will adjourn the house."
The Speaker said she was not against discussion but the issues need to be raised properly in the house.
Kharge, who was then given permission to speak, said he was not raising the issue of cow vigilantism but wanted to raise the matter concerning Scindia, "whose image is being tarnished".
"He is a young leader with 15 years of parliamentary experience. I know him. He can't be anti-Dalit. Many a time, he spoke in favour of the Dalits in this house. It was not good to tarnish his image," Kharge said.
Kharge targetted Ananth Kumar, saying "instead of solving a crisis he instigates it".
He took a dig at former Parliamentary Affairs Minister M Venkaiah Naidu, who is now the National Democratic Alliance's vice presidential candidate.
"Jaisa Naidu sahab karte the, ye bhi waisa hi kar rahe hain (he is doing the same as Naidu used to do)," Kharge remarked.
Ananth Kumar hit back: "Don't give us lessons in parliamentary democracy. Those who have murdered democracy are teaching us parliamentary democracy."
Taking a dig at Kharge, the Minister said the Congress member is an experienced leader "who knows how to ignite fire and douse it".
Kharge later raised the issue of suspension of six Congress MPs for five sittings and demanded that it be revoked.
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