Modi, who called on Khamenei at his office, gifted the Supreme Leader the specially commissioned reproduction of rare 7th Century manuscript of the Holy Quran attributed to Hazrat Ali, the fourth Islamic caliph and first Shia Imam.
Khamenei, a 76-year-old Shia Grand Ayatollah and two-time former president, has the final say over matters related to Iran's foreign policy and key issues.
Written in Kufic script, the manuscript is a prized possession of the Ministry of Culture's at Rampur Raza Library in Uttar Pradesh.
Modi, the first Indian Prime Minister to visit the Islamic Republic after 15 years on a bilateral visit after Atal Bihari Vajpayee, also gifted President Hassan Rouhani specially commissioned reproductions of Mirza Ghalib's collection of poetry in Persian.
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First published in 1863, Kulliyat-e-Farsi-e-Ghalib is a collection of over 11,000 verses by Ghalib.
The reproduction is from a rare copy of the book's 1867 edition to which some missing pages have been added from a copy of the 1872 edition from Maulana Azad's personal collection preserved in the library of Indian Council for Cultural Relations in New Delhi.
Modi's visit comes months after lifting of international sanctions on Iran following Tehran's historic nuclear deal with the Western powers over its contentious atomic programme.