NEW DELHI: Four Indian Supreme Court judges took the unprecedented step of publicly criticising the chief justice on Friday, warning a lack of impartiality could imperil the world's largest democracy.

The judges said they were making their disagreement with Chief Justice Dipak Mishra public after private talks failed to address what they said were serious problems with the running of India's highest court.

They gave no specific details at a hastily arranged press conference.

But in a letter released to the media they said the criticisms related to an alleged lack of transparency in the selection of judges to try cases, calling it a cause for "serious concern".

"The administration of the SC is not in order and many things which are less than desirable have happened in last few months," Justice Jasti Chelameswar, one of the four judges, told reporters.

"Democracy will not survive if judiciary is not impartial," he said.

In a letter to Chief Justice Mishra that has been made public, the judges said they would not divulge details of their concerns to avoid embarrassing the institution.

But one of the four said their concerns related to a case involving the death of a lower court judge, B H Loya, in 2014 days before he was to deliver a final verdict in the case of a senior ruling party politician accused of ordering a murder.

Loya was said to have died of natural causes but the Supreme Court is hearing a petition demanding an investigation into allegations he was murdered.

Mishra did not respond to calls for comment on the allegations.

Experts said it was unprecedented for judges to publicly criticise the head of India's highest court.

The Supreme Court has huge influence in India and has in the past revoked laws passed by the parliament that it considered infringed citizens' rights.

Last year it upheld the fundamental right to privacy of citizens despite government opposition.

There was a mixed reaction from fellow judges, some of whom condemned the four men's actions as irresponsible.

Others were supportive, among them Prashant Bhushan, a Supreme Court lawyer and opposition politician.

"They are doing a service to the nation by letting the country know that the chief justice is abusing and misusing his power as the master of roster to assign cases to particular benches, to junior judges to achieve a predetermined outcome," he said. —AFP