Hangal, 98, passed away in Mumbai this morning following a brief illness aggravated by a fracture in his thigh bone.
"I am deeply saddened by the news of the passing of A K Hangal, one of the most admired character artistes of Hindi cinema," Advani said in his message.
"Hangal sahab represented the best traditions of Bollywood -- its power to capture human pathos, its matchless capacity to promote national unity and integration and, of course, its ability to provide healthy entertainment to the masses," he added.
Advani said that the actor had played diverse roles in films, and excelled in all of them.
"In his demise, at the ripe old age of 98, Indian cinema has lost a towering personality, who was also a highly endearing human being.
I convey my heartfelt condolences to his bereaved family," he said.
BJP President Nitin Gadkari also expressed his grief.
In a condolence message, Gadkari described Hangal as a seasoned actor of the Indian film industry who made a mark in character roles during his career spanning nearly forty years.