The Bharatiya Janata Party also refuted the charges that he was forced to leave the post under pressure from the central government.
"Shevgaonkar has put in his papers due to his alleged involvement in the activities in Mauritius. An independent agency should probe the matter. One cannot escape by resigning and blaming others," BJP national secretary Shrikant Sharma said in a statement.
"IIT Delhi is a honourable institution. No one should politicise the matter by taking its name," he said.
Earlier, Shevgaonkar said he had resigned but refused to divulge the reason.
Reports in a section of media said Shevgaonkar's resignation came under the government's pressure over matters involving cricketer Sachin Tendulkar and BJP leader Subramanian Swamy.
The Aam Aadmi Party (AAP) slammed the government for "misleading" the country on the issue of Shevgaonkar's resignation.
Also read: HRD Ministry denies involvement over IIT-D director's resignation
The government dismissed the report.