Modi shared a 1.21 minute video on Twitter and said Kalam dreamed of an able and capable India of the 21st century and made his own special contribution in this direction.
"As a scientist, he takes the country to greater heights. His life-long efforts were an asset to the nation. Not his words but his personality use to speak a lot.
"In my life also he has been a guide. His work is an inspiration to take the country forward," Modi said in his tweet.
Kalam, an aerospace scientist who served as the 11th President of India between 2002 and 2007, was born on this day on 1931 in Rameswaram, Tamil Nadu.
Union Ministers Amit Shah, Rajnath Singh and Prakash Javadekar also paid tributes to the late leader.
While Shah said Kalam was an epitome of simplicity and knowledge who devoted his entire life to the nation, Singh called him a people's President who would continue to live in the hearts and minds of the people of India.
Kalam's birth anniversary is also celebrated as World Students' Day.
"The birthday of Dr. A.P.J Abdul Kalam - the most popular President of India - is celebrated as World Students Day. He was a real teacher and loved students and even died while delivering a lecture at the Indian Institute of Management, Shillong," Javadekar tweeted.
Delhi Chief Minister Arvind Kejriwal also remembered Kalam, saying "his humble origins and life of compassion for the disadvantaged continues to inspire every Indian".
Kalam's contribution in the field of space sciences has been immense. He also contributed in India's civilian space programme and military missile development, and so he got the title of India's "Missile Man".
He died in July 2015 at the age of 83.
( With inputs from IANS )