In his letter to Vijay Bansal, a resident of Rohini in west Delhi and running a construction business, Modi said he was pleased to have been apprised of the estimate made "according to your inner voice".
Modi's letter was dated March 20, and came in response to Bansal's letter sent March 3.
Bansal has a history of making poll predictions.
In his letter to Modi, Bansal wrote that "two months before the 1984 Lok Sabha elections, I wrote to Rajiv Gandhi on the basis of my inner voice and told him that he will get around 365 seats. The astrologers and opinion polls at that time were talking of 225 seats for him".
After Gandhi got over 400 seats in the polls, he sent a thank you note to Bansal and invited him for tea, according to the letter.
Accpording to Bansal, he told Aam Aadmi Party chief Arvind Kejriwal, whom he claimed to know personally, before the results for December 2013 Delhi assembly elections were out, that he will get around 28 seats when "no opinion poll was giving the AAP more than 6 seats".
"When I told him, he started to laugh. Even he did not believe me," Bansal told IANS.
Bansal said that after AAP got 28 seats, "Kejriwal called me to the Delhi secretariat and we had tea".
Bansal gives around 292 seats to the National Democratic Alliance. He also wrote in his letter that Modi-led NDA will receive the support of "28 other MPs".
While Bansal sent his predictions to Bharatiya Janata Party president Rajnath Singh, and other senior leaders like L.K. Advani, Sushma Swaraj, Arun Jaitley and others, only Modi replied, he said.