"Striking a new chord in the relationship with Mongolia. @narendramodi tries 2 understand intricacies of morin khuur," External Affairs spokesperson Vikas Swarup tweeted.
"In Japan he tried his hand on the drum. In Mongolia PM @narendramodi tries his hand on the morin khuur."
Swarup also posted a picture and video of the smiling Prime Minister holding the wooden-framed trapezoid and trying his hand at creating music from the traditional Mongolian bowed stringed instrument.
Later, Modi also tried his hand at the Yoochin, a box zither-dulcimer with 13 double-wire strings.
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The strings in this traditional Mongolian instrument are struck with two wooden sticks, so-called little wooden hammers and are similar to the 'santur'.
The Prime Minister seemed to be enjoying playing the instrument for a considerable time, wearing a hat and his Mongolian counterpart Chimed Saikhanbile by his side.
Modi also presented Elbegdorj a specially-commissioned reproduction of a rare 13th century manuscript on the history of Mongols considered by many as the first world history.
The manuscript from the Rampur Raza Library, Rampur (Uttar Pradesh) has over 80 fine miniature illustrations. It is a part of Volume 1 of the work and no other copy of it is known to exist.
The breadth of coverage of the work often caused it to be dubbed as the first world history.
Modi, on a two-day visit to Mongolia, the first-ever by an Indian Premier, said he brings the "greetings of your 1.25 billion spiritual neighbours" as he addressed the country's parliament which was specially convened for his visit.