Describing Israel as a real friend, Modi recalled Rivlin's visit to India in November last year.
Hailing the ties between the two nations, Modi said: "...Today it is 'I to I and I for I'. When 'I say I for I, I don't mean the popular saying but what I mean is India with Israel, India for Israel".
Modi, who arrived in Tel Aviv yesterday for a three-day visit, met Rivlin at his residence here.
"It is a privilege to meet President Rivlin again today. I fondly recall his visit to India last November when he charmed us with his affable manner and desire to do more with India," Modi wrote in the guest book at the President's residence.
More From This Section
"President Rivlin is admired in India for his unstinting belief and common good of mankind, I thank him for his friendship and his warm hospitality," wrote Modi, who is the first India prime minister to visit Israel.
Rivlin on his part described Modi as one of the greatest leaders in the world.
"We have a lot in common and doing a lot in common. We understood very well about your thought about the need to help partners who will 'Make in India'," Rivlin said.
"...We are doing a lot in order to fulfill your ideas about 'Make in India'," the Israeli President said.
Rivlin said there was a scope for cooperation between universities and industries of India and Israel.
"The....People in Israel are trying to find ways to invest in India and to make mutual projects together," he said.