Kalam, who would have turned 84 in October, died after suffering a massive cardiac arrest during a lecture at the IIM Shillong yesterday.
"Our former President of India passes away suddenly .. Was delivering a lecture at an IIM, in Shillong and collapsed .. sudden end to an iconic figure...," Bachchan wrote on his blog.
The 72-year-old actor said Kalam put India on the world map in science, missile technology and space research facilities.
"A simple man, of childlike demeanour, practical, caring and endearing to all .. My only achievement of contact with him - a telephone conversation just before he was announced to be the next President of India !! India is grieved," Bachchan wrote.