Hindi and English are India's two official languages for federal government business, although India's constitution recognises a total of 22 languages.
Modi's government has ordered its officials to use Hindi on social media accounts and in government letters. Modi spoke in Hindi and used interpreters in meetings with South Asian leaders last month, and addressed the Bhutanese parliament in Hindi during his first official overseas trip last week.
But with more than half of India's 1.2 billion people using another language as their mother tongue, the push for Hindi risks widening communication divides in a highly diverse country, especially in the southern and eastern states, where local languages or English are preferred.
The chief of the Dravida Munnetra Kazhagam (DMK), a regional party in the southern state of Tamil Nadu, on Thursday slammed India's home ministry for its social media diktat.
The party, born in 1949 of a southern secessionist movement, uses Tamil and English to communicate with voters.
"No one can deny it's beginning to impose Hindi against one's wish. This would be seen as an attempt to treat non-Hindi speakers as second-class citizens," television channels quoted DMK chief M. Karunanidhi as saying.
In the eastern state of Odisha, a member of the state assembly was chastised this week for using Hindi during the question hour. The speaker of the house ordered Kengam Surya Rao to make statements only in English or the local language, Odia.
Anti-Hindi protests in India date back to before the country gained independence in 1947 from former colonial ruler Britain.
Hindi speakers are concentrated in India's northern and central regions, home to the country's two most populous states and where the BJP picked up most of its parliamentary seats in the election. It is the mother tongue of just over 40 percent of Indians, the latest government data show.
In the 1960s the southern DMK party launched a campaign against the government's plan to make Hindi the sole official language, during which Hindi books and effigies of a "Hindi demoness" were burnt on village bonfires.
"Hindi is our official language, we have to promote Hindi," junior home minister Kiren Rijiju said on Thursday, following Karunanidhi's criticism. "It doesn't mean that we undermine the importance of regional languages."
"A DIFFERENT INDIA"
The push for greater use of Hindi by Modi, the son of a poor tea-seller who made a stunning political rise, has been read partly as a move to break from the anglophone elite of the dynastic Congress party, which he thrashed in parliamentary polls in April and May.
"He is trying to represent a different India, which is rural and small-town oriented," said Ajay Gudavarthy, a politics professor at Jawaharlal Nehru University in New Delhi. "That's the group he campaigned to, and that's the group he's from."
Senior members of Modi's Bharatiya Janata Party (BJP) cite some practical reasons too, saying Modi is more at ease in Hindi than English and does not wish to be misunderstood, particularly in interviews. The BJP has long championed Hindi as a uniting force for India.
India's Home Ministry last month ordered all bureaucrats to prioritise Hindi over English on official accounts on social media platforms such as Twitter and Facebook.
Yet India's booming social media scene remains dominated by English, with even Modi still mostly using that language to communicate with the 4.9 million people who follow him there.