Modi also met Moshe's Indian nanny Sandra Samuels, who managed to escape with him from the Nariman House which came under attack by the terrorists, and his grandparents Shimon and Yehudit Rosenberg.
"My visit celebrates the strength of centuries-old links between our societies", Modi said during a welcoming ceremony at Ben Gurion International Airport.
Modi puts his arm around the boy's shoulder and asks him to visit India with his family. I am starting at a lower level.
Talking about the dinner he hosted for Mr Modi, Mr Netanyahu said they also heard an Indian-origin Israeli singer sing a "hauntingly beautiful" Hindi song. "They love India, they love our nation".
With that statement, India officially ended decades of a concealed foreign policy approach to Israel, publicly accepting it as a nation with which it shares a joint future.
Modi makes history by visiting Israel
In today's schedule, the Indian premier will meet with a survivor of the 2008 Mumbai attacks, Israeli child Moshe Holtzberg, along with his Indian nanny Sandra Samuels, according to Indian network News 18. Moshe is the reason I am here in Israel.
"Our goal is to build a relationship that reflects our shared priorities and draws on enduring bonds between our peoples", said Modi, who is the first Indian prime minister to visit Israel. "Throughout the visit, the Indian Prime Minister did not say a word about India's stand on the issue of a Palestinian State", a CPI-M statement said.
"Yad Vashem tells us that those who believe in humanity and civilized values must come together and defend it at all costs". Shri Modi said, "With GST we are aiming towards the economic integration of India".
A Twitter handle affiliated with the Israeli government said: "New fast-growing Israeli [Chrysanthemum] flower named in honor of PM @narendramodi and will be called "MODI". The Prime Minister was accompanied by his counterpart Benjamin Netanyahu.
Explaining the lack of defence deals - India is one of the largest buyers of defence equipment from Israel - Jaishankar said many of those are signed between companies, rather than between countries.