Earlier in the day, the seven-member BCI delegation also met the other three apex court judges, who, along with Chelameswar, had alleged irregularities in the administration of the SC.
"We have been told that there is no crisis".
Justices Sharad Arvind Bobde and L. Nageswara Rao also met Justice Chelameswar at his residence.
"The four senior puisne judges of the Supreme Court have brought to light a serious issue regarding the manner of allocation of cases, particularly sensitive cases, to various benches of the Supreme Court".
He added that the media would be informed about the BCI's day-long parleys with the Supreme Court judges at a press conference tomorrow.
They appreciated the "grave concern" raised by the four Supreme Court judges that cases were not being allocated in a proper manner and "arbitrarily" allocated to "particular designated benches, often headed by junior judges".
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The rebel judges criticised the Chief Justice over allocation of cases, saying the administration of the top court was "not in order".
The BCI chairman, Manan Kumar Mishra, who was heading the delegation, expressed confidence that the rift would be resolved soon.
The apex lawyers' body had yesterday held a meeting to discuss the developments that surfaced after the January 12 press conference by the four seniormost apex court judges. When asked if it was about the petitions seeking a probe into the death of special CBI judge B H Loya, Justice Gogoi replied in the affirmative.
He said that the crucial matters should be listed before a five-judge Constitution bench until the crisis comes to an end. This issue needs to be resolved and clear rules and norms must be laid down for allocation of benches and distribution of cases, which are rational, fair and transparent. "The council has hope and trust that the judges of the Supreme Court will realise the seriousness of the issue and in future may avoid any such situation that politicians or political parties could take undue advantage of and or which could cause harm to our judiciary", the BCI said in a statement on Saturday.
They urged Justice Misra to take immediate steps in this regard. "He should have called a meeting to handle things", the Delhi Bar Association was quoted by news agency ANI.