The party said that Naidu's decision was "illegal and arbitrary" and taken in a "cavalier, cryptic and abrupt manner".
Justice Chelameswar, who represented the four judges in an unprecedented press conference, said they had approached the CJI with a letter but failed to convince him.
The petition says: "None of the reasons given by the Chairman (Venkaiah Naidu)... carry any weight or are legally tenable".
"In the absence of a full-fledged inquiry, it is not possible to return any findings on the same".
Making his submissions, Sibal said chairman Venkaiah Naidu can not summarily reject the notice bearing signatures of 64 MPs and seven former members who had recently retired, on the ground that there was "no proved misbehaviour".More news: Melania Trump unveils her Stage
On 23 April, Naidu, Vice-President of India and Chairman of the Rajya Sabha, had rejected the impeachment motion, holding it was "neither legal nor desirable or proper" to admit it. He states that there was no substantial merit in it. From the reports which are in public domain, the Hon'ble Chairman was not in New Delhi for a good part of the weekend of 21st and 22nd April, 2018.
Earlier on Monday morning, a bench headed by Justice J Chelameswar told senior counsel Kapil Sibal to "come back tomorrow" as the latter mentioned the matter for listing for an early hearing.
"The chairman has no option but to set up the inquiry committee against the CJI once the notice for removal motion was signed by the requisite number of MPs, which in case of RS is 50", said the petition, which was settled by Sibal and filed through advocate Sunil Fernandes. "I am aware of the procedure but it can't be mentioned anywhere else". I have practised in this court for past 45 years. "The misconceived motion for the impeachment of the Chief Justice of India is just one example of this", Jaitley had said.
He also said that the Parliament was supreme in its own jurisdiction and its process can not be subjected to judicial review and "impeachment" motion was filed on untenable grounds for a collateral goal to intimidate the CJI and other judges.
Advocate Bhushan, who appeared along with Sibal, said according to rules, the CJI is disabled to pass any order and only the senior-most judge can decide on the listing of the petition. Moreover, Sibal contended that whether or not there exists evidence to make out a prima facie case is not the job of the Chairman but that of an Inquiry Committee that goes into each allegation. But this petition is against the CJI, who can not decide its listing.