Once a month, India’s prime minister, Narendra Modi, walks into a studio set up at his government bungalow and takes his seat behind a microphone. The air conditioning is switched off to quiet its hum. Thick curtains maintain the room’s silence even from Modi’s favorite peacocks in the garden outside.

Then the prime minister begins his radio show, for which he has recorded more than 100 episodes, with a usual greeting in Hindi: "My dear countrymen, hello!”

What follows — about 30 minutes of Modi playing on-air host to the world’s most populous nation — is one way he has made himself intimately omnipresent across India’s vastness, exerting a hold on the national imagination that seems impervious to criticism of his government’s erosion of India’s democratic norms.