Singhvi also threatened to slap civil and criminal defamation charges against Defence Minister and BJP leader Nirmala Sitharaman if she did not apologise for "false and malicious allegations.
Sitharaman alleged that the Nirav Modi-run Firestone Diamond International had taken on lease a property of Adwait Holdings, a company in which Singhvi's wife is a director.
"What is important is that the premises have been used by Firestar Diamond International," she said.
"Neither Adwait nor my family has any interest with Modi or the company. Last August, the company gave notice to quit tenancy and vacated Kamla Mills premises in December 2017...None of us have anything to do even remotely with Gitanjali company, Firestar or any other business of Nirav Modi," he said.
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The Congress leader said that he had come to the city to attend a wedding and was "aghast" to see news reports of Sitharaman's allegations.
He also threatened defamation case against media outlets carrying "such false and maliciously defamatory allegations".
"None of my family members are share holders or have any interest in the ventures (of Nirav Modi). Should the defence minister make such allegations just because I am a Congress functionary?" he asked.
"The defence minister's statement belonged to absolute gutter-level standard. I know politics is very acrimonious, but there has to be a level in politics," Singhvi said.
"Sensationalism, ignorance and falsehood has exceeded all limits in this irresponsible charge," he said.
The bank subsequently sent two more complaints to the CBI on Tuesday, saying the scam was worth more than Rs 11,400 crore.
The jewellery designer is understood to be a citizen of the country but his brother Nishal and wife Ami are not Indian nationals. They all left India between January 1 and 6, the CBI had said.
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