Navya, 18, is the daughter of Bachchan's daughter Shweta, while four-year-old Aaradhya is his son Abhishek's child.
Bachchan wrote that the two girls enjoy the luxury of a rich legacy but being the fairer sex, they are bound to face judgments and opposition from the society. Nothing, however, should bog them down, said the actor.
"You both carry a very valuable legacy on your tender shoulders - Aaradhya, the legacy of your great-grandfather, Dr Harivansh Rai Bachchan, and Navya, the legacy of your great-grandfather Shri H P Nanda.
The 73-year-old star further wrote that both of them should choose their own path, one which is dictated by their choices not the world's.
"Make your own choices in the light of your own wisdom. Don't let anyone make you believe that the length of your skirt is a measure of your character. Don't let anyone's opinion of who you should be friends with, dictate who you will be friends with.
Towards the end, Bachchan said being a woman is not easy in today's times but he hopes the two girls will change the situation.
"At the end of the day, you are the only one who will face the consequences of your actions, so don't let other people make your decisions for you. Navya - the privilege your name, your surname offers you, will not protect you from the difficulties you will face because you're a woman.
The actor said he would take more pride in being known as their grandfathers than by his own name.
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