Modi, who arrived here this morning to attend the State Funeral Services of Lee who died at the age of 91, had a short meeting with President Rivlin who reiterated an invitation to the Prime Minister to visit Israel.
There is an invitation from Israeli Prime Minister Benjamin Netanyahu for Modi to visit Israel.
But the exact dates and formality on this regard will be decided through diplomatic channels, said External Affairs Ministry Spokesman Syen Akbaruddin.
The two leaders discussed the healthy state of bilateral relation and how to take it forward, he told reporters.
They also discussed the situation in West Asia, official sources said.
Both Modi and Rivlin are in Singapore to attend the state funeral service of Singapore's first Prime Minister Lee Kuan Yew who died last Monday.
Prime Minister Modi had congratulated his Israeli counterpart Benjamin Netanyahu on his re-election recently.
"Congratulations my friend Bibi @netanyahu! Recall our New York meeting last September warmly," Modi had tweeted in Hebrew language.
Netanyahu secured a stunning win against all odds in Israel's closely-fought general elections.
Modi also exchanged notes with Australian Prime Minister Tony Abbott, former US president Bill Clinton, Emir of Qatar Sheikh Tamim bin Hamad al-Thani and Canadian Governor-General David Johnston.
Emir of Qatar last week visited India and held extensive talks with Prime Minister Modi covering entire gamut of bilateral relations as well as regional and international issues after which the two sides signed six agreements.
Modi's interaction with Canadian Governor-General Johnston comes ahead of his visit to Canada next month.