In a condolence message to Dutt's son and Bollywood actor Sanjay Dutt, Kalam, who is a four-nation tour, expressed shock at "the sudden and untimely demise".
"May his soul rest in peace," Kalam said, conveying his condolences to the bereaved family.
"Sunil Dutt had made many significant contributions in the fields of art and public life. I pray to the Almighty to give you and other members of your family the courage and strength to bear this irreparable loss," Kalam wrote to Sanjay Dutt from St. Petersburg.
Dutt, who was sports minister, passed away in Mumbai Wednesday.