It also sought a restraint on the Centre from acting on Supreme Court's collegium recommendation recently for elevating three High Court Chief Justices and a senior lawyer to the apex court.
The plea was mentioned for urgent listing before a bench of justices Badar Durrez Ahmed and Sanjeev Sachdeva which asked "how can this recommendation be challenged".
The bench also declined to list the matter for hearing today despite a spirited attempt made by a Mumbai-based lawyer, Mathews J Nedumpara, when it was informed that a similar plea was likely to come up for hearing tomorrow.
In his plea, the petitioner also urged for a declaration that selection and appointment of judges of the apex court and High Court be made by advertising the vacancies to invite applications from all eligible candidates.
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He said that hundreds and thousands of lawyers are of the view that appointment to such offices should be open to all eligible candidates and only "the best ought to be selected and appointed".
Nedumpara has also said that the applications received should be processed by a competent authority through "an open and transparent mechanism".
The collegium also recommended the appointment of former Additional Solicitor General and senior advocate L Nageswara Rao as a Supreme Court judge.
The apex court's current strength of judges is 25, against the sanctioned strength of 31. With the elevation of three High Court Chief Justices and Rao the strength will go upto 29.
He has also sought to "prohibit and restrain the Union of India from acting upon any such recommendation made by the collegium, and further to stay all further appointment of Judges till the collegium system is improved and rendered defect-free and foolproof."
The petitioner has also urged the court to declare that "no selection and appointment of Judges of the Supreme Court and the High Courts be made except by notification of the vacancies and invitation of applications from all eligible candidates."
The plea alleged that "a large section of the legal fraternity and the public at large, of the higher judiciary being dominated by the kith and kin of sitting and former Judges of the Supreme Court and High Courts, celebrity lawyers, Chief Ministers, Governors.