It began with the Congress vice president taking a swipe at Modi, saying he was not in a position to lead by example on his counsel against self-promotion.
"Leading by example is clearly overrated," Gandhi said on Twitter, after Modi told bureaucrats yesterday not to use social media for self-promotion or spend too much time online.
Smriti Irani fired a retaliatory salvo at the Congress vice president with a tweet, "Look who is talking about being overrated". The tweet was accompanied by a smiley.
The prime minister actively uses the social media to connect with the public and is the most followed leader on Twitter and Instagram in the country.
Modi has 29.3 million followers on Twitter and has emerged as the most followed world leader on photo-sharing app Instagram with a whopping 6.9 million followers, surpassing US President Donald Trump.