Another PIL was filed by a Maharashtra-based journalist Banduraj Sambhaji Lone in the apex court. They had also sent a copy of the letter to the acting Chief Justice of Bombay High Court.
The bench, however, said it will look into the petitions but will also consider the objections raised.
Brijgopal Harkishan Loya, the judge presiding over the CBI special court in Mumbai, died between the night of 30 November and the early morning of 1 December 2014, while on a trip to Nagpur.
President Shantaram Naik on Saturday demanded that the criminal case in which Bharatiya Janata Party (BJP) National President Amit Shah was one of the accused should be re-opened in view of the press conference held by the four judges of the Supreme Court in the national capital on Friday.
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Poonawala, in his plea, contended that circumstances revolving around the death of the judge were "questionable, mysterious and contradicting".
The issue came under the spotlight in November previous year after media reports quoting his sister fuelled suspicion about the circumstances surrounding his death and its link to the Sohrabuddin case.
The four Collegium judges only wanted the CJI to follow the "well-settled and time-honoured conventions" of the Supreme Court while assigning cases to various Benches to facilitate a "disciplined and efficient transaction of business of the court".
"In the PIL concerning the death of Judge Loya, we believe that the matter must be entrusted to the senior-most judges of the Supreme Court who should ensure that under their supervision there is a thorough and impartial investigation of the case by an independent SIT", it said.
In addition to the petitions before the apex court, two similar writ petitions are also pending before Bombay High Court, one by the Bombay Lawyers' Association, and other by one Suryakant Lodge. They have also made a point about Judge Loya's case and I think that is also something that needs to be investigated properly. The matter was argued by advocate Varinder Kumar Sharma.