Congress president Rahul Gandhi said the points highlighted by the judges were "extremely important" and called for a probe into Loya's case by the "highest level of the Supreme Court".
The Congress said the PIL concerning the death of Loya must be entrusted to the senior-most judges of the apex court who should ensure that under their supervision there is a "thorough and impartial" investigation by an independent SIT.
BJP chief Amit Shah was an accused in the case but was discharged.
One of the four senior-most judges, who held an unprecedented press conference, had said that the matter involving Loya's death was one of the issues underpinning their differences with Chief Justice Dipak Misra.
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"I think the points that have been raised by the four judges are extremely important. They have mentioned there is a threat to democracy. It needs to be looked into carefully.
In his brief statement, Gandhi said that all citizens who love the idea of justice and believe in the Supreme Court were looking at the developments, and therefore it was important that those were addressed.
A battery of senior Congress politician-lawyers including Kapil Sibal, P Chidambaram, Manish Tewari, Vivek Tankha and Salman Khurshid were present at the press conference. Senior party leaders Ahmed Patel, AICC general secretary in-charge of Maharashtra Mohan Prakash and its chief spokesperson Randeep Singh Surjewala were also present.
"The Congress earnestly appeals that the Full Court of the Supreme Court should take up the issues raised by the four the judges and find solutions that are consistent with the traditions and conventions of the judiciary pointed out by the judges and that will preserve the independence of the judiciary," it said.
CPI(M) general secretary Sitaram Yechury said a thorough investigation was required to understand how the independence and integrity of the judiciary was getting "affected", after the judges said many "less than desirable" things had taken place in the apex court.
He said it was necessary for the three wings of democracy -- the executive, the legislature and the judiciary - to ensure that whatever issues had been raised were corrected.
"It is a dark day for democracy that even the judges are working under pressure and without independence," he said.
Four senior judges of the Supreme Court today virtually revolted against Chief Justice of India Dipak Misra, listing a string of problems that they said were afflicting the country's highest court, and warned those could destroy Indian democracy.
Meanwhile, the CPI today clarified that its member D Raja visited Justice J Chelameswar, one of the four judges, in his personal capacity and not as a representative of the party.
"Raja went in his personal capacity and not as a representative of the party", CPI general secretary S Sudhakar Reddy told PTI.
Reddy also said it was a "misunderstanding" that his party wanted to meddle in the controversy.
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