Shevgaonkar has resigned with more than two years of his tenure left amid a controversy over the circumstances under which he quit including alleged pressure put on him by the Human Resources Development Ministry.
Shevgaonkar sent his resignation in a letter to Chairman of IIT Board of Governors Vijay P Bhatkar on Friday evening in which he cited "personal reasons".
AAP said that BJP's "unjustified political interference" is trampling the autonomy of the top institutions for professional and technical education.
"Is it not a fact that impolite language was used against such a senior professor and is it also not fact that he was humiliated in that meeting?" the party said in a statement.
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The party alleged that the BJP was hell bent on imposing its "dangerous agenda" on the nation.
"Ranging from the removal of the Chief Vigilance Officer of AIIMS to the shocking resignation of the IIT Delhi Director, the entire government appears hell bent on imposing its dangerous agenda on the nation.