By enabling tweets to be sent out as an SMS, any Indian with a mobile device, with or without a data plan, is able to receive messages from political leaders and government bodies. Mobile users can activate the service through a missed call to an assigned phone number.
"People who sign up will receive a set of curated Tweets based on the highest engagement throughout the day to stay up-to-date with real-time information about government-related news, policies and activities," Twitter said.
Read MoreCramer: Twitter flies higher for the long haul
"And you can use Twitter Samvad during emergency situations to receive live updates from government bodies, such as time-sensitive information and details about rescue efforts," it said.
So far, a total of 16 political leaders and ministries are linked up to Twitter Samvad. Modi was the first leader to kick off the service.
Twitter Samvad is built on the technology of ZipDial, a Bangalore-based mobile marketing and analytics company that Twitter acquired in January.
Political parties including the ruling Bharatiya Janata Party and the Indian National Congress partnered with Twitter and ZipDial to offer a similar service during 2014's general election to make their Twitter accounts accessible to all mobile users in India.
More recently, some local news outlets offered SMS tweets during the presentation of the government's annual budget on February 28.
Twitter's service of SMS tweets activated by a missed call is currently only available in India although the company is looking to roll out the service in other emerging markets.