Bachchan earned the best actor honour for his delightful performance as a hypochondriac father in Shoojit Sircar's "Piku".
The president called Bachchan "living legend" while raving about the mix of veterans and newcomers in the list of winenrs at this year's National Awards.
"Back from Delhi and National Award! So humbled and touched, for President of India to take my name in his speech!" the 73-year-old actor tweeted.
Bachchan was accompanied by his family to the ceremony. It was his fourth National award and son Abhishek Bachchan, daughter-in-law Aishwarya Rai Bachchan, wife Jaya Bachchan and daughter Shweta Nanda turned up at the ceremony here to cheer for the actor.