The two awards have come as a boost to the critically- acclaimed "Newton", which will represent India in the Best Foreign Language category at the 90th Academy Awards next year.
Rao, who has a broken ankle, said coming to the awards gala despite the injury, turned out to be worthwhile.
"This is very encouraging... It inspires me to work harder everyday. Congratulation to fellow nominees, your performances have inspired all of us. Let us keep doing this beautiful work making these wonderful stories. Let us keep doing that. Here is to cinema," he said in his acceptance speech.
This was to give tributes to his mother, who passed away while he was shooting for the film.
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"It was a hard time for us to make this film. When I was shooting for this film, my dear mother passed away. We were shooting in the forests of Chhattisgarh.
"It is because of her blessings, I believe that 'Newton' is getting all these appreciations. So thank you mom and I love you," Rao said.
Writer Mayank Tewari and director Amit V Masurkar shared the award for the best screenplay at the ceremony where Australia's "Sweet Country" won the top award.
India's "Lady of the Lake" by director Haobam Paban Kumar won a special mention in the Cultural Diversity Award Under the Patronage of UNESCO category in which "Dede" was the winner.