"Prime Minister Narendra Modi knows everything. He has no need for experts like Raghuram Rajan," said Gandhi in a tweet.
In another tweet, he thanked Rajan for his role in steering the country's economy in "difficult times".
"Thank you Dr Rajan for steering the economy in difficult times. People like you make India great," another post on his twitter handle @OfficeOfRG said.
Earlier, RBI Governor Raghuram Rajan today said no to a second term, in a surprise announcement putting at rest all speculation over his continuance.