The bar association will also address the press later in the day.
The bar association today expressed his disapproval over the manner in which the press conference was conducted, stating that "just creating doubts in the minds of people will not serve the interest of the judiciary."
"If they had to come for a press conference then they should have said something substantial. Just creating doubts in the minds of people will not serve the interest of the judiciary. This was not properly planned. They didn't say anything about justice Loya," Vikas Singh, Supreme Court Bar Association president said.
The Bar Council of India also threw its weight behind the chief justice.
The chairman of the Bar Council of India said the judges should not have held a press conference on a "minor issue of roster". He said a delegation from the council would meet the senior judges and the chief justice of India tomorrow and request them not to bring such issues before the public.
"Holding a press conference on a minor issue of the roster is saddening. We have a meeting at 5pm today and tomorrow our delegation will meet those senior judges, CJI and other judges and request them to not bring issues like these in front of public," Manan Kumar Mishra, Chairman, Bar Council of India said.
On Friday, in an unprecedented development, the top court's four next highest-ranking judges, Justices Kurian Joseph, Chelameswar, Ranjan Gogoi and Madan Lokur, had criticised the distribution of cases by the chief justice to judges and raised concerns about judicial appointments. They said all top judges should be involved in setting the procedures used to hire and promote judges in all the country's courts, they added.
The judges said the issues involving its administration were serious enough to prompt them to go public.
"The four of us are convinced that unless this institution is preserved and it maintains its equanimity, democracy will not survive in this country," Justice Jasti Chelameswar told a news conference.
The judges did not give specific details of their concerns during the press conference, but said "it is an issue of assignment of a case".
When reporters asked whether it was related to the case of a lower court judge B Loya, who died in December 2014 while hearing the sensitive Sohrabuddin Sheikh 'fake encounter' case, one of the four judges said "yes". BJP President Amit Shah is also an accused in the case.
The justices released a letter they had written to Misra in which they mentioned cases of "far-reaching consequences for the nation and the institution" that were selectively assigned by the chief justice without rational "basis for such assignment".
(With inputs from agencies)
The bar association will also address the press later in the day