Modi, who was at the fourth spot till last week, has overtaken Indonesian President S B Yudhoyono on Thursday on the popular micro-blogging site, with 5.09 million followers.
Obama has 43.9 million followers, while the Pope and Yudhoyono have over 14 million and 5.08 million followers, respectively.
"This shows how Mr Modi has been actively using Twitter to connect with the masses reinforcing the tool of digital diplomacy in a larger context making the social media platform a powerful channel for communicating and engaging with all Indians across the country," Twitter said in a statement.
On Wednesday, Facebook COO Sheryl Sandberg, who is on a five-day trip to India, said Modi is the second most popular world leader on Facebook with about 18.9 million 'likes' against his name, after Obama.
Twitter said there were nearly 60 million elections- related Tweets during the Lok Sabha elections this year.
"Narendra Modi was the top elections-related term on Twitter during the entire polling period, more than AAP and INC combined. On counting day itself, Modi and BJP accounted for over half of the two million elections-related tweets," it added.
Modi's Twitter account (@narendramodi) has grown by more than one million followers since his election win, while the official account of the Prime Minister's office (@PMOIndia) has grown more than 40 percent since his swearing-in ceremony.
His election victory tweet "India has won!" remains the most retweeted tweet of all time from India.
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