The position has been vacant since May 28, when the apex court sent former National Accountability Bureau (NAB) chairman Fasih Bokhari packing.
A three-judge bench led by Chief Justice Iftikhar Chaudhry resumed hearing the case today and said sufficient time had been given to the government for the key appointment.
Chaudhry remarked that the appointment of the Chairman was a serious issue and the government was not taking it seriously.
Attorney General Munir A Malik said the government wants to appoint a reputed and experienced individual as the anti-graft chief and several names were being considered. He sought more time from the court to complete the process.
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The apex court adjourned the case till September 13.
Leader of Opposition in the National Assembly, Khursheed Shah, said his Pakistan People's Party was yet to reach a consensus with other parties on who would head the NAB.