Singhvi announced his decision to resign from the posts in a statement issued Monday evening, in which he said he had quit to prevent "even the slightest possible parliamentary disruption".
Quick to cash in on the controversy, the Bharatiya Janata Party (BJP) said Singhvi should explain in parliament why he had quit as chairman of the parliamentary committee, which is looking into the Lokpal bill, among others.
"It is a serious matter and the party has not given any statement on the issue. As he has resigned from the post of chairman of the parliamentary standing committee, we hope he will make a statement on why has he resigned," BJP leader Arun Jaitley said.
BJP spokesperson Prakash Javadekar said the matter "is nothing less than a casting couch" and Singhvi should explain.
The Congress MP said in the statement that "canards and baseless allegations" were being spread about an alleged inappropriate conversation in the CD that took the social media by storm following a high court directive that it should not be published or telecast by the mainstream media.
He, accordingly, informed Congress chief Sonia Gandhi about his decision "not to brief the press" and his resignation as chairperson of the parliamentary standing committee on law, justice and personnel.
"I have done this only to prevent even the slightest possible parliamentary disruption regarding the purported CD being circulated about me. Since I am a disciplined party soldier, I did not think it fit to subject the party to any inconvenience on this account. All allegations are patently baseless and false."
Singhvi, an eminent lawyer, accused sections of print and visual media of spreading falsehoods about contents of the CD by repetition and hearsay that there is reference in the CD to the promise of any post and said there was no reference to any illegality, corrupt practice, or wrongdoing.
"People inimically opposed to me, who have assiduously spent over 10 days hearing, seeing, amplifying and distilling the CD have found no vestige of any reference, not even remotely, to any illegality, corrupt practice, or wrongdoing.
"No one has heard any such reference in the CD. There is none simply because it does not exist. It is pure imagination, wishful thinking and sensationalism," Singhvi said.
He said the CD raises no public interest issues but has evoked salacious private and prurient interest and demanded that privacy issues be respected.
"It is lamentable that such canards are being spread about a CD which has, in fact, been accepted thrice over to be fabricated and morphed," he added.
The Congress leader said a reputed media house, which was co-defendant in the suit also recorded a consent statement based on the statement of the author of the CD and a final permanent decree of injunction has been passed over five days ago.
Congress media cell chief Janardhan Dwivedi said that it did not matter whether the party had sought Singhvi's resignation or he had quit on his own, but he had taken the correct step.
Party spokesperson Rashid Alvi, meanwhile, said Singhvi had resigned on "moral grounds" despite a court injunction against the releasing the contents of the CD.
Alvi also attacked BJP over its MLAs and Ministers in Gujarat and Karnataka having allegedly watched a porn video inside the respective assemblies, saying the opposition party should not give lessons on morality.
Maharashtra Pradesh Congress Committee cultural cell vice chief Guru S. Nair, however, called for Singhvi's resignation as MP too.
"He should resign from parliament too, because his presence will only cause disruption of proceedings," Nair said.
Meanwhile, Delhi Bar Council member and former president of the Delhi Bar Association Rajiv Khosla said the CD row involving Singhvi has harmed the dignity of the legal profession.
"The Delhi lawyers are, therefore, interested to the truth as to why an advocate's driver stooped too low to make this dirty CD," he added.
Singhvi said in his statement, that the canard was spread to give the issue a public interest flavour "since otherwise the contents of the CD, assuming them to be true (which they certainly are not), would disclose only something private and consensual giving a cause of action only to aggrieved family members (who have stood completely by me) and to no one else."
Stressing that privacy issues should be respected, he said: "Either the CD is morphed or it is not. In either event it raises no public interest issue, yet evokes salacious private and prurient interest and contumacious internet violation of a flagrant kind. As a political or a professional class, instead of gleefully watching, promoting or participating in a person's natural and understandable discomfiture, we must respect privacy issues."
In October 2010, Singhvi had been temporarily removed from his post of spokesperson for his decision to appear in a lottery case in the Kerala High Court. Singhvi was reinstated after one and a half months.