Rao, 84, died here on Wednesday following a heart attack.
In her message, Sonia Gandhi described Rao a legal luminary and conveyed her condolences to Rao's family.
Rahul Gandhi tweeted: "My deepest condolences on the demise of legal luminary P.P. Rao. Leaves a huge void in the legal fraternity & is a great personal loss."
Rao has appeared before the Supreme Court in several landmark cases. He had also appeared for the Central Bureau of Investigation during the UPA government in the case challenging the Allahabad High Court's verdict on dropping conspiracy charge against BJP leader L.K. Advani and 19 others in the Babri Masjid demolition case.
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