Kakodkar, who resigned as chairman of the board of governors of IIT-Bombay in March following differences with the HRD ministry, had said that the process to select directors of these prestigious seats of learning was casual in nature.
"I strongly protest that kind of an allegation. Paper work will show that within the legal framework, everything was done as per rules," Irani told reporters at a news conference here.
Irani said, "To cast aspersions on the office of the President of the country, a Visitor of IITs, is extremely unfortunate".
IIT-Delhi director R Shevgaonkar resigned last December with more than two years of his tenure left amid a controversy over alleged pressure by the HRD ministry on him.
The appointment of directors was relating to three IITs, IIT-Bhubaneshwar, IIT-Patna and IIT-Ropar, the selection of which was now complete.