Modi, who visited the Yad Vashem Museum and honoured the victims of the Holocaust, was suggested by Netanyahu, apparently spontaneously, that they visit the grave of Herzl born Benjamin Ze'ev Herzl - which lies adjacent to the memorial.
Prime Minister Modi agreed on the suggestion and the two leaders visited the marble tomb at Mt. Herzl.
Modi placed a small rock on the marble tomb as Netanyahu watched with a smile.
It also posted a brief video that showed Modi placing his hand on the tomb.
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"Before departing the Yad Vashem complex the leaders visited the Grave of Theodor Herzl - Chozeh HaMedinah (lit. "Visionary of the State")," Ministry of External Affairs spokesperson Gopal Baglay tweeted.
Herzl was an Austro-Hungarian journalist, playwright, political activist, and writer who is considered the founding father of Zionism - a movement to establish a Jewish homeland.