The BJP, meanwhile, claimed the Indian economy is doing “most poorly” among major economies in the world.
Venkaiah Naidu said Prime Minister Narendra Modi has got every right to choose an officer of his choice.
He cited reports about the adverse comments made against Gupta by his seniors in the past to question his credibility.
“How do they know there is no pressure on me?” said Dr Sharma in response to the allegations leveled at him.
In his letter sent to new Health Minister and AIIMS president Dr Harsh Vardhan also, Gupta mentioned the two cases.
AIIMS officials said there was no evidence that any pressure from outside was put on Gupta to alter the autopsy report.
Sunanda Pushkar was found dead on Jan 17, 2014 under mysterious circumstances in the Hotel Leela Palace.
Delhi Police is investigating the case after the SDM asked them to probe it.
Tharoor asserted that he had been demanding thorough, rapid and transparent investigation into the case.
Tharoor’s letter comes against the backdrop of strong criticism from Congress MP Mani Shankar Aiyar calling him “immature” and a “chameleon.
Tharoor had praised Modi saying he was looking to turn himself from a “hate figure into an avatar of modernity and progress”.
Tharoor, however, added that Modi’s message had not trickled down, referring to the killing of a young Muslim IT professional in Pune.
He described the Prime Minster as “Modi 2.0″ which he said has replaced “Modi 1.0″.
Dealing in detail with each of the point in the agenda, he wondered as to what purpose the document would serve.
Shashi Tharoor said that there are certain rules for the security of persons in which Congress has no role.