Ms Pushkar was found dead in a suite of a five-star hotel in south Delhi on January 17, 2014.
The court has also asked the centre to clarify its view on BJP leader Subramanian Swamy's petition asking for a court-monitored probe by the CBI-led Special Investigation Team.
Mr Swamy has alleged an "inordinate delay" in the investigation "which is a blot on the justice system".
The court, according to PTI, replied, "Neither his (Tharoor's) party is in power nor he is a minister anymore."
The petition seeks a multi-disciplinary Special Investigation Team of the Intelligence Bureau, the Enforcement Directorate, RAW, the Delhi Police and headed by the CBI to inquire into Ms Pushkar's death.
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