In a letter and a press conference, the judges said Chief Justice Dipak Misra was assigning cases to benches of his preference, breaching court rules.
Democracy would not survive in India unless the court’s regulations were followed, they added.
This is the first time Supreme Court judges have ever addressed the media.
By convention, they have not spoken directly to press in the past, so as to appear impartial in court cases.
The unprecedented event has prompted India’s Prime Minister Narendra Modi to hold an emergency meeting with Law Minister Ravi Shankar Prasad.
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The four judges circulated a letter they had addressed to the chief justice, accusing him of assigning cases with “far-reaching consequences for the nation” and the court selectively to benches “with no rationale” – effectively implying that he had sought to influence the outcome.
They also expressed their unhappiness with “certain judicial orders” passed by the court, which they claimed “adversely affected the overall functioning of the court”.
The chief justice’s role was “not a recognition of any superior authority” over his colleagues, they added.
They said they had no choice but to “address the nation” because the chief justice had “refused to listen to their concerns” earlier.
There was no specific mention of which cases they felt had been assigned to benches selectively. However Indian media speculate that the issue could be in relation to the handling of a case of alleged corruption by a retired high court judge late last year.
Critics said the chief justice had worked to ensure only judges he approved of could hear the case – raising concerns of interference in the judiciary.
The controversy led to a petition calling for an independent investigation into the corruption charges instead.