The Centre had earlier told the apex court that the Appointments Committee of the Cabinet was looking into the matter and the process of filling up vacancies was at an advanced stage.
Chief Justice (CJI) J S Khehar, who heading a bench also comprising Justice D Y Chandrachud, said, "I will try to expedite the things at my level. Let us see."
Justice Khehar made the observation when the counsel for the petitioner alleged that the vacancies were not being filled up and the work was being affected at the tribunals.
It was dealing with a PIL filed by one Akshay Pundir which has contended that "adhocism has become order of the day as many of the posts of senior vice presidents and vice presidents have not been filled up".
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Solicitor General Ranjit Kumar, appearing for the Centre, rebutted the allegations of the petitioner that a CBI inquiry was pending against the ITAT chairperson.
He said a "wrong assertion" has been made in this regard by the petitioner "as the CBI inquiry was dropped way back in April 2014 against the person in question".
However, senior advocate Meenakshi Arora, appearing for petitioner, alleged that a person against whom a CBI inquiry was going on has been allowed to continue as the ITAT chairperson.
The court had earlier pulled up the Centre over the delay in the appointments, saying that the ITAT was one of the key sources of revenue earning for the government, which was still moving at a snail's pace in filling up the vacancies.
The petition has said that "the timely appointment of presidents, vice-presidents and members will go a long way in tackling the burgeoning tax litigation in the country".