The inquiry by will not deal with the allegations of sexual harassment against the CJI.
After the meeting, the CJI and the four judges went ahead with their listed business.
A roster of the work for fresh cases notified under the order of the chief justice of India will come into effect from February 5 till further orders.
Justice Gogoi lamented that the very issues which give a different identity to a community make its people hate those who are different.
Chief Justice of India Ranjan Gogoi said it is 'very very serious' if people were unable to approach the high court.
The court also asked the Uttar Pradesh authorities to file a status report by Thursday on the accident of the Unnao rape case victim.
Justice S A Bobde, who is heading the inquiry panel, has appointed Justice Malhotra to the committee.
Chief Justice of India Ranjan Gogoi on Monday said it was in "our best interest" to heed the advice of the Constitution as not doing so would result in a "sharp descent into chaos".
Speculations surrounding Justice Gogoi's appointment as the next CJI emerged following the unprecedented press conference of 4 most-senior judges.
'Not providing a copy to the complainant while holding her complaint to be unfounded would be a violation of the principles of natural justice and a complete travesty of justice'
A five-judge Constitution bench headed by Chief Justice Ranjan Gogoi upheld the 2010 Delhi high court verdict and dismissed three appeals filed by Secretary General of the Supreme Court and the Central Public Information officer of the apex court.
It is the custom in the top court that a retiring judge, on his last day, is given the honour of sitting with the CJI in the majestic Court no 1.
A notice by the office of Supreme Court Secretary General also said that the report of the committee constituted as part of the in-house procedure is not liable to be made public.
The 5-judge bench, was referring to four senior most judges of apex court -- Justices J Chelameswar, Ranjan Gogoi, M B Lokur and Kurian Joseph -- who had held January 12 press conference against CJI Dipak Misra raising litany of questions on allocation of cases.
"Go to the Supreme Court," said the bench to NGO Anti Corruption Council of India, which had said publication of allegations against the CJI directly hit the Indian judicial system.
"Why is it that whenever there are no political overtones to a case, the CBI does a good job?" he said.
The former Supreme Court employee dubbed on Tuesday as "very frightening" the atmosphere of the in-house inquiry committee and "walked out" raising various objections including denial of her lawyer's presence.
The meeting between the CJI and four judges -- Justices J Chelameswar, Ranjan Gogoi, Madan B Lokur and Kurian Joseph -- lasted for around 10-15 minutes before resumption of court proceedings at 10:30 am, court sources said.
The woman said that she will consult her lawyer and decide on the next steps.
The Supreme Court on Friday said it will take a decision on the early listing of petitions challenging the Centre's decision to abrogate provisions of Article 370 which had given a special status to Jammu and Kashmir.
The order will be passed by a five-judge Constitution bench of Chief Justice Ranjan Gogoi, Justices NV Ramana, DY Chandrachud, Deepak Gupta and Sanjiv Khanna on a petition filed by a Supreme Court Secretary-General challenging the January 2010 judgment of the Delhi high court.
None of the four judges -- Justices J Chelameswar, Ranjan Gogoi, M B Lokur and Kurian Joseph -- feature in the list of members of the 5-judge constitution bench.
The judgment stated that there cannot be "any distrust about the responsibilities" the Chief Justice discharges.
The apex court's observation came when senior advocate Indira Jaising, appearing for a woman devotee, Bindu Ammini, alleged violation of the 2018 verdict and said her client was attacked for her bid to enter the shrine.
The meeting was being attended by Chief Justice Ranjan Gogoi and leader of the Congress in Lok Sabha Mallikarjun Kharge, they said.
The former CJI said the statements made by the individual do not mean that entire institution has crumbled.
Justice Ranjan Gogoi, who will demit office as the Chief Justice of India in a week's time, has etched his name in the annals of history by giving finality to one of the most politically and religiously sensitive cases, the Ayodhya land dispute, which dates back to even before the Supreme Court came into existence in 1950.
A protest march was held at Mandi House against the enquiry procedure adopted in the sexual harassment complaint against Chief Justice of India Ranjan Gogoi.
Good judges are going away. We need replacements. The younger lot in the bar are not willing to become judges, says the CJI.
The Supreme Court of India on Wednesday said it would consider a plea for early listing of petitions challenging the Centre's decision to abrogate provisions of Article 370 which had given special status to Jammu and Kashmir.
The apex court will have to re-constitute a five-judge bench to hear the pleas after Dussehra vacation as the ex-CJI Ramana and Justice R Subhash Reddy, who were part of the five-judge bench which had heard the pleas, have retired.
The court agreed to re-constitute a five-judge bench to hear pleas after summer vacation.
Since the CJI was a part of the bench and author of the Tuesday's verdict which reinstated Verma as the CBI Director, he opted himself out of the panel's meeting which was ordered to be convened within a week.
"For women, the Pegasus scandal is deeply concerning, for speaking out against the state and men in positions of state power has meant that their lives are wrecked by such surveillance permanently.
Justice Karnan said the eight judges have "jointly committed the offences punishable under the SC/ST Atrocities Act of 1989 and amended Act of 2015.
A bench comprising CJI and Justice Sanjiv Khanna was hearing a PIL filed by NGO Common Cause challenging the appointment of Rao as interim CBI director.
The letter narrates the incidents of July 7-8 when some people allegedly associated with Sengar, the sitting BJP legislator, threatened the victim's family with dire consequences.
Both Hindus and Muslim parties have filed review pleas against the verdict that paved way for a Ram temple at the disputed while giving 5-acre land for a mosque elsewhere.
Verdicts paving the way for construction of a Ram Temple at Ayodhya and India's multi-billion dollar Rafale fighter jet deal with France were 2019's landmark imprints of the Supreme Court, which also found itself at the centre of a controversy with then Chief Justice of India Ranjan Gogoi being accused of sexual harassment before getting the clean chit.
The year 2022 is going to be the second year since the inception of the top court in 1950 which will see three different CJIs in as many months.