"I am saying this from deep within. Like a father caring for his son...," he said turning emotional, Press Trust of India reported.
"'Modi ji, you will have to rest for half day,' Pranab da would say. 'Why are you running around so much; you must cut down on your programmes. You will have to take care of your health'," he said.
"It was during the UP polls that he told me that win and loss happen all the time but will you take care of your body or not? It was not part of his responsibilities as the President but it was the humane person inside him which cared for a friend," the Prime Minister said.
President Mukherjee too expressed his "deep gratitude and appreciation" for PM Modi.
"It (difference in political views) did not affect the relationship between the President and the Prime Minister, between the titular head and the actual head of the administration," President Mukherjee said.
President Pranab Mukherjee's tenure as the first citizen ends on July 24. A closely-watched election to find his successor will be held on July 17 when members of an electoral college consisting of parliamentarians and legislators will choose between Ram Nath Kovind, backed by the ruling BJP-led government, and Meira Kumar, supported by Congress-led Opposition parties. Votes will be counted on July 20.